excecutive report

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Descriptive Statistics

Data
Executive Salary Age Gender Education Promotions Pay
1 79 49 Female Bachelors 4 Low
2 76 38 Female Associates 0 Low
3 83 60 Male Masters 4 High
4 92 63 Male Masters 6 High
5 80 55 Female Bachelors 3 Low
6 81 54 Female Masters 6 High
7 77 42 Male Masters 4 Low
8 87 59 Male Masters 6 High
9 69 42 Male Bachelors 1 Low
10 70 36 Female Bachelors 1 Low
11 73 48 Male Associates 2 Low
12 80 53 Male Associates 2 Low
13 81 46 Female Associates 2 High
14 87 57 Male Masters 4 High
15 78 49 Female Associates 1 Low
16 78 40 Female Masters 2 Low
17 77 55 Male Masters 4 Low
18 81 48 Male Bachelors 5 High
19 75 42 Female Associates 1 Low
20 83 52 Male Bachelors 3 High
21 74 41 Female Bachelors 2 Low
22 85 62 Male Masters 3 High
23 86 53 Male Bachelors 5 High
24 73 36 Female Associates 0 Low
25 70 44 Male Associates 2 Low
26 81 50 Female Bachelors 3 High
27 77 50 Male Bachelors 3 Low
28 85 60 Male Associates 3 High
29 69 39 Female Associates 0 Low
30 73 48 Female Associates 2 Low
31 91 59 Male Masters 5 High
32 75 44 Male Bachelors 3 Low
33 90 64 Male Masters 5 High
34 74 42 Female Bachelors 0 Low
35 72 46 Female Bachelors 1 Low
Summary Statistics
Quantitative Variables Qualitative Variables
Salary Age Promotions Gender Frequency % Rel. Freq.
N 35.000 35.000 35.000 Female 16 45.7%
Mean 78.914 49.314 2.800 Male 19 54.3%
Standard Deviation ERROR:#NAME? ERROR:#NAME? ERROR:#NAME? 35 100.0%
Variance ERROR:#NAME? ERROR:#NAME? ERROR:#NAME?
Standard Error ERROR:#NAME? ERROR:#NAME? ERROR:#NAME? Education Frequency % Rel. Freq.
Margin of Error (95%) ERROR:#NAME? ERROR:#NAME? ERROR:#NAME? Associates 11 31.4%
Bachelors 13 37.1%
Minimum 69.000 36.000 0.000 Masters 11 31.4%
P10 ERROR:#NAME? ERROR:#NAME? ERROR:#NAME? 35 100.0%
Q1 74.000 42.000 1.500
Median 78.000 49.000 3.000 Pay Frequency % Rel. Freq.
Q3 83.000 55.000 4.000 Low 21 60.0%
P90 ERROR:#NAME? ERROR:#NAME? ERROR:#NAME? High 14 40.0%
Maximum 92.000 64.000 6.000 35 100.0%
Mode 81.000 42.000 3.000
Range 23.000 28.000 6.000
Interquartile Range 9.000 13.000 2.500
Coefficient of Variation ERROR:#NAME? ERROR:#NAME? ERROR:#NAME?
Skewness 0.332 0.148 0.157
Kurtosis -0.642 -0.996 -0.853
Salary
Salary (by 5)
Bin Bin Frequency Relative Frequency
Mean 78.914 70 66-70 4 11.4%
Standard Error 1.068 75 71-75 8 22.9%
Median 78.000 80 76-80 9 25.7%
Mode 81.000 85 81-85 8 22.9%
Standard Deviation 6.317 90 86-90 4 11.4%
Sample Variance 39.904 91-95 2 5.7%
Kurtosis -0.642 35 100.0%
Skewness 0.332
Range 23.000
Minimum 69.000
Maximum 92.000
Sum 2762.000
Count 35.000
Age
Age (by 5)
Bin Bin Frequency Relative Frequency
Mean 49.314 40 36-40 12 34.3%
Standard Error 1.361 45 41-45 9 25.7%
Median 49.000 50 46-50 6 17.1%
Mode 42.000 55 51-55 5 14.3%
Standard Deviation 8.050 60 56-60 3 8.6%
Sample Variance 64.810 61-65 0 0.0%
Kurtosis -0.996 35 100.0%
Skewness 0.148
Range 28.000
Minimum 36.000
Maximum 64.000
Sum 1726.000
Count 35.000
Promotions
Promotions (by 1)
Bin Bin Frequency Relative Frequency
Mean 2.800 1 0-1 16 45.7%
Standard Error 0.303 2 1-2 7 20.0%
Median 3.000 3 2-3 5 14.3%
Mode 3.000 4 3-4 4 11.4%
Standard Deviation 1.795 5 4-5 3 8.6%
Sample Variance 3.224 5-6 0 0.0%
Kurtosis -0.853 35 100.0%
Skewness 0.157
Range 6.000
Minimum 0.000
Maximum 6.000
Sum 98.000
Count 35.000
Gender
Education
Pay
Salary by Age
Covariance ERROR:#NAME?
Correlation Coefficient 0.846
R-Square 0.715
Salary by Promotions
Covariance ERROR:#NAME?
Correlation Coefficient 0.774
R-Square 0.599
Pay by Gender
Count of Pay Column Labels Count of Pay Column Labels
Row Labels High Low Grand Total Row Labels High Low Grand Total Odds of Pay=High
Female 3 13 16 Female 18.75% 81.25% 100.00% Female 0.231
Male 11 8 19 Male 57.89% 42.11% 100.00% Male 1.375
Grand Total 14 21 35 Grand Total 40.00% 60.00% 100.00%
Pay by Education
Count of Pay Column Labels Count of Pay Column Labels
Row Labels High Low Grand Total Row Labels High Low Grand Total Odds of Pay=High Odds Ratio Log Odds Ratio
Associates 2 9 11 Associates 18.2% 81.8% 100.00% Associates 0.222 0.071 -2.639
Bachelors 4 9 13 Bachelors 30.8% 69.2% 100.00% Bachelors 0.444 0.154 -1.872
Masters 8 3 11 Masters 72.7% 27.3% 100.00% Masters 2.667 4.000 -1.386
Grand Total 14 21 35 Grand Total 40.00% 60.00% 100.00%

&"Calibri,Italic"&A

Salary Histogram

Relative Frequency

66-70 71-75 76-80 81-85 86-90 91-95 0.11428571428571428 0.22857142857142856 0.25714285714285712 0.22857142857142856 0.11428571428571428 5.7142857142857141E-2

Salary (k$)

% Relative Frequency

Salary by Age Scatter Diagram

Age

79 76 83 92 80 81 77 87 69 70 73 80 81 87 78 78 77 81 75 83 74 85 86 73 70 81 77 85 69 73 91 75 90 74 72 49 38 60 63 55 54 42 59 42 36 48 53 46 57 49 40 55 48 42 52 41 62 53 36 44 50 50 60 39 48 59 44 64 42 46

Age

Salary (k$)

Salary by Promotions Scatter Diagram

Promotions

79 76 83 92 80 81 77 87 69 70 73 80 81 87 78 78 77 81 75 83 74 85 86 73 70 81 77 85 69 73 91 75 90 74 72 4 0 4 6 3 6 4 6 1 1 2 2 2 4 1 2 4 5 1 3 2 3 5 0 2 3 3 3 0 2 5 3 5 0 1

Age

Salary (k$)

Age Histogram

Relative Frequency

36-40 41-45 46-50 51-55 56-60 61-65 0.34285714285714286 0.25714285714285712 0.17142857142857143 0.14285714285714285 8.5714285714285715E-2 0

Age (Years)

% Relative Frequency

Promotions Histogram

Relative Frequency

0-1 1-2 2-3 3-4 4-5 5-6 0.45714285714285713 0.2 0.14285714285714285 0.11428571428571428 8.5714285714285715E-2 0

Promotions

% Relative Frequency

Gender Pie Chart

Female Male 0.45714285714285713 0.54285714285714282

Gender Bar Graph

Female Male 0.45714285714285713 0.54285714285714282

% Relative Frequency

Education Bar Graph

Associates Bachelors Masters 0.31428571428571428 0.37142857142857144 0.31428571428571428

% Relative Frequency

Education Pie Chart

Associates Bachelors Masters 0.31428571428571428 0.37142857142857144 0.31428571428571428

Pay Bar Graph

Low High 0.6 0.4

% Relative Frequency

Pay Pie Chart

Low High 0.6 0.4

Probability Distributions

Discrete Distributions Continuous Distributions
(k=8) (p=.2) (n=6 p=.2) (μ=3) (a=30 b=100) (μ=50 σ=5) (μ=1/3) Seed=1039 (a=0 b=1)
D. Uniform Bernoulli Binomial Poisson C. Uniform Normal Exponential x Pr C. Uniform
4 1 4 1 38.035 43.993 0.722 1 0.125 0.115
1 1 3 3 42.113 45.289 0.585 2 0.125 0.173
5 1 0 0 40.034 44.673 0.647 3 0.125 0.143
8 0 1 3 46.659 46.436 0.479 4 0.125 0.238
8 1 1 6 38.028 43.990 0.722 5 0.125 0.115
8 0 0 3 97.979 59.488 0.010 6 0.125 0.971
1 0 2 2 67.631 50.472 0.207 7 0.125 0.538
4 1 0 3 40.169 44.715 0.643 8 0.125 0.145
7 0 1 2 83.046 53.496 0.092 0.758
2 1 0 5 32.989 41.399 1.051 0.043
2 1 0 4 32.307 40.805 1.137 0.033
1 0 0 6 57.298 48.603 0.314 0.390
1 0 1 3 47.306 46.584 0.466 0.247
2 0 2 4 75.915 52.007 0.141 0.656
2 0 2 4 78.507 52.521 0.122 0.693
1 0 1 2 77.511 52.321 0.129 0.679
3 0 3 2 49.041 46.966 0.434 0.272
3 0 1 1 87.150 54.509 0.068 0.816
5 0 1 4 84.760 53.900 0.082 0.782
3 0 2 3 91.055 55.685 0.046 0.872
3 0 2 1 85.022 53.964 0.080 0.786
3 0 1 3 68.898 50.700 0.196 0.556
8 1 1 6 31.910 40.388 1.200 0.027
4 0 2 6 88.011 54.746 0.063 0.829
4 0 2 5 72.094 51.284 0.170 0.601
3 0 1 4 84.307 53.791 0.085 0.776
8 0 1 1 44.463 45.909 0.526 0.207
7 0 0 5 48.065 46.753 0.452 0.258
8 0 3 2 96.665 58.341 0.016 0.952
3 1 1 3 42.758 45.466 0.567 0.182
8 0 0 7 63.435 49.720 0.246 0.478
1 0 0 3 55.631 48.290 0.335 0.366
6 0 0 0 78.079 52.435 0.125 0.687
7 0 1 2 53.510 47.881 0.364 0.336
8 0 1 5 54.230 48.021 0.354 0.346
4 0 2 4 70.026 50.905 0.186 0.572
3 0 0 6 46.808 46.470 0.476 0.240
7 0 0 4 54.839 48.139 0.345 0.355
3 0 1 4 77.900 52.399 0.126 0.684
7 1 3 1 35.407 42.881 0.854 0.077
1 1 1 4 33.420 41.720 1.006 0.049
2 0 0 7 50.925 47.363 0.403 0.299
1 0 0 2 79.278 52.679 0.117 0.704
3 0 1 2 70.143 50.926 0.185 0.573
4 0 1 1 69.225 50.759 0.193 0.560
5 0 0 5 83.632 53.631 0.089 0.766
3 0 0 3 50.404 47.255 0.411 0.291
8 0 1 3 90.280 55.427 0.050 0.861
1 0 1 6 64.578 49.924 0.235 0.494
2 0 2 4 81.354 53.119 0.103 0.734
1 0 0 3 72.668 51.391 0.165 0.610
8 0 2 6 76.855 52.191 0.134 0.669
1 0 1 4 65.747 50.134 0.224 0.511
3 1 1 3 42.183 45.309 0.583 0.174
7 0 1 4 56.138 48.386 0.328 0.373
6 0 2 9 61.673 49.403 0.264 0.452
7 0 1 2 96.291 58.083 0.018 0.947
6 0 1 3 63.501 49.732 0.246 0.479
1 0 1 4 79.481 52.721 0.116 0.707
2 0 1 1 61.288 49.333 0.268 0.447
7 0 1 2 83.892 53.692 0.087 0.770
6 0 1 4 45.249 46.102 0.508 0.218
2 0 1 5 98.932 60.816 0.005 0.985
4 0 1 4 83.843 53.681 0.087 0.769
5 0 3 3 58.569 48.838 0.299 0.408
6 0 0 3 49.017 46.961 0.434 0.272
5 0 0 3 69.744 50.853 0.189 0.568
2 0 1 5 88.470 54.876 0.060 0.835
8 0 1 2 73.226 51.495 0.161 0.618
6 0 0 5 90.184 55.396 0.050 0.860
5 0 1 1 88.558 54.902 0.059 0.837
7 0 1 5 91.953 56.003 0.041 0.885
7 1 1 3 32.442 40.933 1.119 0.035
3 0 3 2 65.249 50.045 0.229 0.504
2 0 1 4 60.120 49.122 0.281 0.430
7 0 1 1 92.290 56.129 0.039 0.890
1 0 1 3 70.485 50.988 0.183 0.578
1 0 1 4 61.585 49.387 0.265 0.451
7 1 1 1 36.796 43.508 0.777 0.097
6 0 2 2 73.918 51.625 0.155 0.627
8 0 2 3 54.441 48.062 0.351 0.349
8 0 0 1 71.775 51.225 0.172 0.597
8 1 0 2 34.324 42.300 0.928 0.062
5 0 2 2 44.206 45.844 0.532 0.203
5 1 1 2 43.435 45.646 0.550 0.192
6 0 1 5 59.712 49.047 0.286 0.424
4 0 1 3 52.226 47.627 0.382 0.318
2 0 0 4 85.986 54.205 0.074 0.800
1 0 0 2 69.850 50.873 0.188 0.569
7 1 3 3 30.684 38.324 1.543 0.010
6 0 2 3 82.320 53.332 0.097 0.747
6 0 5 4 95.717 57.724 0.021 0.939
5 0 0 2 93.499 56.617 0.032 0.907
2 0 1 6 72.606 51.379 0.165 0.609
8 0 0 4 63.790 49.783 0.243 0.483
4 1 3 2 32.070 40.564 1.174 0.030
2 1 4 5 34.689 42.507 0.901 0.067
2 0 1 7 90.585 55.527 0.048 0.866
3 0 3 7 58.229 48.776 0.303 0.403
3 0 3 0 64.550 49.919 0.235 0.494
3 1 3 1 37.107 43.636 0.762 0.102
7 1 2 1 42.012 45.261 0.588 0.172
6 1 2 2 43.093 45.556 0.559 0.187
3 0 1 1 46.847 46.479 0.475 0.241
8 0 3 4 96.467 58.201 0.017 0.950
1 0 1 2 44.390 45.891 0.527 0.206
6 0 0 4 87.028 54.477 0.068 0.815
4 0 4 4 84.655 53.874 0.082 0.781
5 0 3 2 45.838 46.244 0.495 0.226
3 1 2 2 43.021 45.537 0.561 0.186
3 0 0 4 95.465 57.579 0.022 0.935
7 0 2 1 82.581 53.391 0.095 0.751
7 0 1 3 83.662 53.638 0.089 0.767
6 0 2 0 90.835 55.610 0.047 0.869
7 0 1 1 99.972 66.775 0.000 1.000
8 1 1 1 39.887 44.626 0.652 0.141
5 1 2 3 35.266 42.810 0.862 0.075
6 0 0 5 87.458 54.593 0.066 0.821
8 0 0 3 69.752 50.855 0.189 0.568
3 0 0 3 99.712 63.210 0.001 0.996
7 0 1 1 53.971 47.971 0.357 0.342
5 0 2 4 99.756 63.494 0.001 0.997
7 0 1 4 78.767 52.574 0.120 0.697
4 0 3 2 91.483 55.833 0.043 0.878
2 1 1 0 42.585 45.419 0.572 0.180
7 1 1 2 41.038 44.980 0.616 0.158
3 0 0 1 86.885 54.438 0.069 0.813
6 0 4 1 91.194 55.732 0.045 0.874
6 0 2 1 81.310 53.109 0.104 0.733
4 1 2 3 41.100 44.998 0.614 0.159
3 0 2 3 98.520 60.153 0.007 0.979
1 0 1 2 59.259 48.965 0.291 0.418
8 0 2 2 52.976 47.776 0.371 0.328
3 0 1 0 74.277 51.693 0.153 0.633
5 0 1 1 97.178 58.735 0.014 0.960
4 0 1 4 80.583 52.953 0.108 0.723
8 0 2 3 51.532 47.487 0.393 0.308
8 1 0 2 37.725 43.877 0.735 0.110
7 0 3 5 99.387 61.878 0.003 0.991
8 1 1 2 36.588 43.421 0.788 0.094
5 0 1 4 44.728 45.975 0.520 0.210
6 1 3 4 37.112 43.637 0.762 0.102
4 0 3 4 76.379 52.097 0.137 0.663
1 0 0 4 93.867 56.778 0.031 0.912
8 0 0 1 96.947 58.551 0.015 0.956
4 1 2 3 41.891 45.227 0.591 0.170
1 0 0 1 87.035 54.478 0.068 0.815
7 0 2 4 69.107 50.738 0.194 0.559
7 1 2 3 43.098 45.557 0.559 0.187
6 0 0 5 67.332 50.418 0.210 0.533
6 0 1 2 90.483 55.493 0.049 0.864
3 1 1 1 35.057 42.703 0.876 0.072
7 0 1 0 59.541 49.016 0.288 0.422
6 0 0 4 45.554 46.176 0.501 0.222
7 0 0 3 61.801 49.426 0.263 0.454
1 0 2 4 87.159 54.512 0.068 0.817
6 1 2 4 42.933 45.513 0.563 0.185
8 0 1 1 52.694 47.720 0.375 0.324
1 0 1 3 89.280 55.115 0.055 0.847
5 0 1 4 95.527 57.614 0.022 0.936
8 0 1 2 82.989 53.483 0.093 0.757
8 0 2 5 54.392 48.053 0.351 0.348
5 0 3 1 96.635 58.319 0.016 0.952
5 0 1 6 92.027 56.030 0.040 0.886
8 0 0 3 80.036 52.837 0.112 0.715
4 0 3 3 46.849 46.480 0.475 0.241
3 0 0 3 58.667 48.856 0.298 0.410
7 0 1 4 87.078 54.490 0.068 0.815
4 0 2 2 93.375 56.564 0.033 0.905
7 1 0 4 35.561 42.956 0.844 0.079
6 0 1 6 73.762 51.595 0.157 0.625
8 1 1 4 35.885 43.109 0.825 0.084
4 1 0 4 31.280 39.547 1.334 0.018
2 0 0 2 98.979 60.905 0.005 0.985
1 1 0 3 41.690 45.170 0.597 0.167
1 0 2 2 78.808 52.583 0.120 0.697
5 0 2 5 58.703 48.863 0.297 0.410
5 0 3 7 49.233 47.008 0.431 0.275
4 0 3 6 60.132 49.124 0.281 0.430
5 0 1 5 95.516 57.608 0.022 0.936
5 0 2 4 53.484 47.876 0.364 0.335
8 0 2 4 57.182 48.581 0.315 0.388
5 0 1 3 98.368 59.948 0.008 0.977
2 0 2 2 97.669 59.172 0.011 0.967
1 0 1 3 47.133 46.545 0.469 0.245
5 0 1 5 73.867 51.615 0.156 0.627
7 0 0 5 61.585 49.387 0.265 0.451
1 0 1 0 79.756 52.779 0.114 0.711
3 0 0 1 51.019 47.382 0.401 0.300
6 0 1 1 45.655 46.200 0.499 0.224
4 0 2 2 64.223 49.861 0.239 0.489
3 0 0 2 82.818 53.444 0.094 0.755
4 0 1 1 83.969 53.711 0.087 0.771
3 0 3 5 85.223 54.013 0.079 0.789
2 0 1 0 65.789 50.141 0.224 0.511
6 0 1 2 70.722 51.032 0.181 0.582
5 0 1 8 62.181 49.494 0.259 0.460
8 0 3 3 75.552 51.937 0.143 0.651
5 0 0 0 87.609 54.634 0.065 0.823
5 0 2 4 93.698 56.703 0.031 0.910
5 0 0 5 87.407 54.579 0.066 0.820
5 1 1 3 39.150 44.385 0.678 0.131
4 0 1 5 93.916 56.800 0.030 0.913
1 0 2 3 58.772 48.875 0.296 0.411
5 0 1 3 94.315 56.985 0.028 0.919
5 0 2 3 49.665 47.099 0.423 0.281
7 0 1 3 55.749 48.312 0.333 0.368
2 0 2 2 71.871 51.243 0.171 0.598
6 0 2 4 93.019 56.415 0.035 0.900
5 1 1 1 38.099 44.016 0.719 0.116
5 0 1 1 51.068 47.392 0.400 0.301
7 1 0 2 41.201 45.028 0.611 0.160
8 1 1 2 37.661 43.852 0.737 0.109
1 0 1 2 90.801 55.599 0.047 0.869
1 0 1 3 79.549 52.736 0.115 0.708
6 0 1 1 66.620 50.290 0.216 0.523
8 0 0 3 67.007 50.360 0.212 0.529
2 0 0 1 51.401 47.460 0.395 0.306
1 0 0 2 75.469 51.921 0.144 0.650
2 0 3 7 94.719 57.182 0.026 0.925
5 0 0 6 78.000 52.419 0.126 0.686
6 0 0 3 73.941 51.629 0.155 0.628
2 0 0 3 77.152 52.249 0.132 0.674
2 0 1 2 84.258 53.779 0.085 0.775
6 0 0 3 78.188 52.457 0.124 0.688
5 0 0 2 99.293 61.613 0.003 0.990
3 0 1 9 56.381 48.431 0.325 0.377
5 0 2 1 71.653 51.203 0.173 0.595
2 0 1 0 67.996 50.537 0.204 0.543
2 1 3 3 42.138 45.296 0.584 0.173
7 0 1 7 66.236 50.221 0.219 0.518
8 0 1 0 51.235 47.426 0.398 0.303
3 0 0 4 58.733 48.868 0.297 0.410
4 0 2 1 60.673 49.222 0.275 0.438
5 0 3 3 70.790 51.044 0.180 0.583
8 1 0 3 39.910 44.634 0.652 0.142
6 0 0 1 97.330 58.863 0.013 0.962
8 1 2 5 36.165 43.237 0.810 0.088
5 0 1 5 45.078 46.061 0.512 0.215
8 1 1 4 30.968 38.989 1.427 0.014
3 0 1 2 63.670 49.762 0.244 0.481
2 0 4 0 84.657 53.875 0.082 0.781
8 0 1 3 58.836 48.887 0.296 0.412
7 0 2 0 66.689 50.303 0.215 0.524
1 0 1 4 91.553 55.858 0.043 0.879
8 1 1 3 37.904 43.944 0.727 0.113
4 0 0 3 92.356 56.154 0.039 0.891
2 0 1 1 64.431 49.898 0.237 0.492
1 0 3 3 49.113 46.982 0.433 0.273
2 0 2 5 65.819 50.147 0.223 0.512
6 0 0 7 67.992 50.537 0.204 0.543
7 0 2 5 45.935 46.267 0.493 0.228
4 0 1 1 49.720 47.111 0.422 0.282
4 0 1 3 97.513 59.026 0.012 0.964
5 0 2 2 55.689 48.301 0.334 0.367
3 0 0 6 54.473 48.068 0.350 0.350
7 0 1 4 79.265 52.677 0.117 0.704
3 0 2 4 73.236 51.497 0.161 0.618
8 0 1 1 85.994 54.207 0.074 0.800
7 0 1 1 59.562 49.020 0.287 0.422
6 0 4 3 80.746 52.988 0.107 0.725
2 0 1 4 84.305 53.790 0.085 0.776
7 0 1 6 88.975 55.024 0.057 0.842
8 1 1 4 43.931 45.774 0.538 0.199
2 0 3 8 52.151 47.612 0.384 0.316
4 0 0 2 53.254 47.831 0.367 0.332
1 0 1 4 92.519 56.217 0.038 0.893
8 0 1 4 82.408 53.352 0.096 0.749
7 0 2 4 98.517 60.150 0.007 0.979
5 1 0 2 41.406 45.088 0.605 0.163
1 0 1 1 78.404 52.500 0.123 0.691
6 0 0 3 47.445 46.615 0.463 0.249
6 0 1 3 64.123 49.843 0.240 0.487
8 0 2 5 66.009 50.181 0.222 0.514
2 0 1 1 49.611 47.088 0.424 0.280
8 0 2 3 80.940 53.030 0.106 0.728
3 0 3 2 85.774 54.151 0.076 0.797
2 0 1 4 94.164 56.914 0.029 0.917
1 0 1 4 57.300 48.603 0.314 0.390
8 0 1 3 67.054 50.368 0.212 0.529
2 0 0 3 83.087 53.506 0.092 0.758
8 0 3 3 75.706 51.966 0.142 0.653
1 1 3 3 40.878 44.932 0.621 0.155
3 0 2 2 85.723 54.138 0.076 0.796
1 0 1 1 86.721 54.395 0.070 0.810
8 0 0 4 52.267 47.635 0.382 0.318
5 0 1 4 69.652 50.837 0.189 0.566
6 0 1 4 81.530 53.157 0.102 0.736
7 0 3 2 50.504 47.276 0.409 0.293
8 0 1 9 64.634 49.934 0.235 0.495
4 0 0 2 69.400 50.791 0.192 0.563
2 0 1 1 97.633 59.137 0.011 0.966
3 0 1 1 68.387 50.608 0.200 0.548
7 1 1 1 35.676 43.011 0.837 0.081
7 1 3 3 42.425 45.375 0.576 0.177
6 0 2 2 79.457 52.716 0.116 0.707
1 0 1 3 62.136 49.486 0.260 0.459
1 0 1 5 50.953 47.368 0.402 0.299
4 0 3 2 74.418 51.720 0.152 0.635
3 1 0 2 37.802 43.906 0.731 0.111
3 0 2 7 70.756 51.038 0.180 0.582
7 0 5 3 94.256 56.957 0.029 0.918
2 0 0 3 86.627 54.370 0.071 0.809
4 0 1 2 66.080 50.193 0.221 0.515
4 0 0 3 67.526 50.453 0.208 0.536
8 0 3 2 80.205 52.873 0.111 0.717
1 0 0 2 96.766 58.414 0.016 0.954
2 0 1 2 91.354 55.788 0.044 0.876
4 0 2 3 85.625 54.113 0.077 0.795
2 0 0 3 81.166 53.078 0.104 0.731
1 1 0 0 37.084 43.626 0.764 0.101
1 1 0 4 43.884 45.762 0.539 0.198
6 0 0 0 68.253 50.584 0.201 0.546
3 0 0 0 50.592 47.294 0.408 0.294
6 1 2 2 33.044 41.442 1.045 0.043
1 0 1 4 44.843 46.003 0.517 0.212
8 0 3 7 84.219 53.770 0.085 0.775
1 0 0 4 60.032 49.106 0.282 0.429
3 0 2 5 51.032 47.385 0.401 0.300
2 1 2 5 36.924 43.561 0.771 0.099
4 0 1 6 44.907 46.019 0.516 0.213
5 0 0 4 72.000 51.267 0.170 0.600
8 0 0 2 98.564 60.217 0.007 0.979
3 0 3 4 67.477 50.444 0.208 0.535
2 0 1 3 53.568 47.892 0.363 0.337
2 0 2 1 55.824 48.326 0.332 0.369
6 0 2 3 95.394 57.539 0.023 0.934
8 0 1 1 88.923 55.009 0.057 0.842
1 1 1 4 32.858 41.295 1.066 0.041
7 0 1 2 98.769 60.533 0.006 0.982
8 1 0 2 38.998 44.333 0.684 0.129
3 0 2 3 66.073 50.192 0.221 0.515
5 1 0 2 41.615 45.148 0.599 0.166
2 0 1 1 59.509 49.010 0.288 0.422
7 0 2 2 72.839 51.423 0.164 0.612
5 0 0 3 95.097 57.377 0.024 0.930
5 0 0 1 66.723 50.309 0.215 0.525
2 0 2 7 96.225 58.040 0.018 0.946
4 1 0 6 30.848 38.733 1.471 0.012
7 0 2 4 63.771 49.780 0.243 0.482
4 0 1 2 71.092 51.099 0.178 0.587
7 0 1 2 76.458 52.113 0.137 0.664
2 0 2 3 96.603 58.297 0.017 0.951
7 0 2 4 97.750 59.251 0.011 0.968
8 0 1 2 63.619 49.753 0.244 0.480
1 1 1 1 40.942 44.951 0.619 0.156
6 0 1 5 50.592 47.294 0.408 0.294
1 0 1 2 62.493 49.551 0.256 0.464
5 0 1 1 62.126 49.484 0.260 0.459
7 0 2 1 78.586 52.537 0.122 0.694
7 0 0 1 74.025 51.645 0.155 0.629
5 0 2 3 65.599 50.107 0.225 0.509
2 0 1 2 65.155 50.028 0.230 0.502
6 1 0 4 34.777 42.555 0.895 0.068
6 0 1 1 92.628 56.259 0.037 0.895
7 0 1 5 89.158 55.079 0.056 0.845
2 1 2 2 43.615 45.693 0.546 0.194
6 0 3 2 70.252 50.946 0.184 0.575
8 0 2 0 68.857 50.693 0.196 0.555
5 0 1 1 66.879 50.337 0.214 0.527
3 0 1 3 68.171 50.569 0.202 0.545
5 1 0 2 42.634 45.432 0.571 0.180
8 0 2 9 45.956 46.272 0.493 0.228
1 0 1 2 75.636 51.953 0.143 0.652
5 0 0 5 93.345 56.551 0.033 0.905
4 0 1 2 57.911 48.717 0.306 0.399
7 1 2 2 42.324 45.348 0.579 0.176
8 0 1 1 66.150 50.206 0.220 0.516
8 0 0 6 74.238 51.685 0.153 0.632
1 0 2 4 93.988 56.833 0.030 0.914
7 0 2 7 69.605 50.828 0.190 0.566
6 0 0 3 62.463 49.545 0.256 0.464
7 0 1 3 76.851 52.190 0.134 0.669
6 0 1 1 63.510 49.733 0.246 0.479
4 0 1 2 92.931 56.380 0.035 0.899
8 0 0 3 44.916 46.021 0.515 0.213
6 0 1 1 77.889 52.396 0.127 0.684
4 1 3 7 38.165 44.040 0.716 0.117
4 0 0 1 66.806 50.324 0.214 0.526
4 0 3 2 96.308 58.094 0.018 0.947
1 0 2 4 95.040 57.347 0.025 0.929
6 1 1 5 41.632 45.153 0.598 0.166
5 0 0 4 74.999 51.830 0.147 0.643
6 0 0 2 95.932 57.854 0.020 0.942
4 0 1 0 63.617 49.752 0.244 0.480
7 1 0 0 43.363 45.627 0.552 0.191
8 0 0 3 77.932 52.405 0.126 0.685
8 1 0 3 31.166 39.359 1.365 0.017
1 1 3 2 30.551 37.926 1.615 0.008
6 0 1 2 50.404 47.255 0.411 0.291
4 0 2 4 65.988 50.177 0.222 0.514
2 0 1 4 71.307 51.139 0.176 0.590
7 0 2 4 81.619 53.177 0.102 0.737
8 0 0 5 89.423 55.159 0.055 0.849
8 0 1 2 52.170 47.616 0.383 0.317
5 0 0 4 73.343 51.517 0.160 0.619
3 0 1 3 82.888 53.460 0.093 0.756
4 0 2 2 46.138 46.315 0.489 0.231
2 0 1 5 72.553 51.369 0.166 0.608
5 0 1 4 44.339 45.878 0.529 0.205
4 0 1 3 52.286 47.639 0.382 0.318
6 0 3 3 64.352 49.884 0.237 0.491
1 0 1 3 47.962 46.731 0.453 0.257
6 1 3 3 40.145 44.708 0.644 0.145
7 0 0 2 52.264 47.634 0.382 0.318
2 0 1 4 71.733 51.217 0.172 0.596
6 0 0 3 95.332 57.505 0.023 0.933
6 0 1 0 45.089 46.063 0.512 0.216
7 0 2 3 69.447 50.800 0.191 0.564
4 0 1 1 44.597 45.942 0.523 0.209
5 0 2 4 92.164 56.081 0.040 0.888
3 0 0 1 62.356 49.526 0.257 0.462
6 1 2 3 32.241 40.740 1.147 0.032
8 0 1 4 68.819 50.686 0.197 0.555
4 0 1 3 62.517 49.555 0.256 0.465
2 0 2 4 49.733 47.114 0.422 0.282
2 0 1 1 82.352 53.339 0.097 0.748
7 0 3 4 59.079 48.932 0.293 0.415
8 0 1 3 47.996 46.738 0.453 0.257
3 0 2 4 70.434 50.979 0.183 0.578
2 0 2 0 61.081 49.296 0.271 0.444
7 0 1 3 83.662 53.638 0.089 0.767
5 0 2 6 52.147 47.611 0.384 0.316
6 0 1 2 83.638 53.633 0.089 0.766
8 0 1 2 76.430 52.107 0.137 0.663
3 1 1 3 36.943 43.569 0.770 0.099
2 0 3 2 51.713 47.523 0.390 0.310
8 0 2 2 94.486 57.067 0.027 0.921
4 0 2 3 61.869 49.438 0.262 0.455
1 0 1 4 96.806 58.444 0.016 0.954
7 1 2 3 33.175 41.541 1.031 0.045
1 0 0 4 88.195 54.798 0.062 0.831
3 0 2 0 52.769 47.735 0.374 0.325
1 0 0 3 79.109 52.644 0.118 0.702
2 0 1 6 48.037 46.747 0.452 0.258
6 0 2 3 47.966 46.732 0.453 0.257
5 0 0 2 71.384 51.153 0.175 0.591
1 1 1 3 36.475 43.372 0.794 0.093
8 1 3 2 35.260 42.807 0.863 0.075
5 1 0 4 41.412 45.090 0.605 0.163
8 0 0 2 86.364 54.302 0.072 0.805
4 0 1 4 73.521 51.550 0.158 0.622
4 1 1 2 34.328 42.302 0.928 0.062
5 0 1 6 45.148 46.078 0.510 0.216
1 0 2 2 57.708 48.679 0.309 0.396
2 0 1 3 45.727 46.218 0.498 0.225
8 0 1 1 47.330 46.589 0.465 0.248
5 0 2 3 52.258 47.633 0.382 0.318
3 1 0 5 43.104 45.559 0.559 0.187
3 0 1 2 54.187 48.013 0.354 0.346
2 1 2 3 33.531 41.797 0.996 0.050
8 0 1 6 62.329 49.521 0.258 0.462
8 0 0 2 96.601 58.295 0.017 0.951
7 0 1 2 93.341 56.549 0.033 0.905
4 0 1 2 64.881 49.979 0.232 0.498
2 0 2 4 78.725 52.566 0.121 0.696
4 0 3 6 75.522 51.931 0.143 0.650
4 1 1 3 43.946 45.778 0.538 0.199
3 0 0 3 75.843 51.993 0.141 0.655
7 0 1 3 62.790 49.604 0.253 0.468
4 0 0 5 66.610 50.288 0.216 0.523
6 0 1 4 48.464 46.841 0.444 0.264
7 0 1 2 76.039 52.031 0.140 0.658
5 1 0 5 39.684 44.561 0.659 0.138
1 0 3 1 77.276 52.274 0.131 0.675
5 0 4 5 80.993 53.041 0.106 0.728
6 0 2 4 49.135 46.987 0.432 0.273
4 0 1 3 95.514 57.607 0.022 0.936
1 0 2 3 52.946 47.770 0.372 0.328
1 0 1 2 79.028 52.628 0.119 0.700
2 0 0 8 56.358 48.427 0.326 0.377
5 1 1 2 40.466 44.807 0.633 0.150
3 0 1 2 56.405 48.436 0.325 0.377
8 0 0 6 79.150 52.653 0.118 0.702
4 0 2 8 48.154 46.773 0.450 0.259
7 0 1 2 87.633 54.641 0.065 0.823
8 0 0 7 60.096 49.117 0.281 0.430
3 1 1 1 43.882 45.762 0.539 0.198
1 1 1 1 42.376 45.362 0.578 0.177
2 0 2 5 82.194 53.304 0.098 0.746
5 0 2 5 97.310 58.846 0.013 0.962
5 0 1 4 81.891 53.237 0.100 0.741
7 1 1 2 32.438 40.929 1.119 0.035
1 1 0 1 30.658 38.253 1.556 0.009
2 0 1 2 83.187 53.529 0.092 0.760
5 0 1 4 48.695 46.891 0.440 0.267
5 0 2 2 73.922 51.626 0.155 0.627
4 0 2 4 94.871 57.259 0.025 0.927
4 0 1 2 51.500 47.480 0.393 0.307
8 0 2 4 70.115 50.921 0.186 0.573
7 0 2 4 52.999 47.781 0.371 0.329
1 0 1 1 70.425 50.978 0.183 0.578
3 0 0 2 48.109 46.763 0.451 0.259
4 0 0 3 65.604 50.108 0.225 0.509
2 0 3 3 75.172 51.863 0.146 0.645
4 0 1 4 84.219 53.770 0.085 0.775
5 0 1 2 77.084 52.236 0.132 0.673
2 0 2 3 93.674 56.693 0.032 0.910
7 0 2 1 67.746 50.492 0.206 0.539
4 0 1 5 80.810 53.002 0.107 0.726
D. Uniform (k=8)
(by 1)
D. Uniform Population Bin Bin Frequency Rel. Freq Population
1 1 62 0.124 0.125
Mean 4.624 4.500 2 2 61 0.122 0.125
Standard Error 0.105 3 3 54 0.108 0.125
Median 5.000 4 4 60 0.120 0.125
Mode 8.000 5 5 66 0.132 0.125
Standard Deviation 2.340 6 6 57 0.114 0.125
Sample Variance 5.478 5.250 7 7 66 0.132 0.125
Kurtosis -1.268 More 74 0.148 0.125
Skewness -0.065 500 1.000 1.000
Range 7.000
Minimum 1.000
Maximum 8.000
Sum 2312.000
Count 500.000
Bernoulli (p=.2)
(by 1)
Bernoulli Population Bin Bin Frequency Rel. Freq Population
0 0 411 0.822 0.800
Mean 0.178 0.200 1 1 89 0.178 0.200
Standard Error 0.017 500 1 1
Median 0.000
Mode 0.000
Standard Deviation 0.383
Sample Variance 0.147 0.160
Kurtosis 0.855
Skewness 1.689
Range 1.000
Minimum 0.000
Maximum 1.000
Sum 89.000
Count 500.000
Binomial (n=6 p=.2)
(by 1)
Binomial Population Bin Bin Frequency Rel. Freq Population
0 0 122 0.244 0.262
Mean 1.230 1.200 1 1 210 0.420 0.393
Standard Error 0.045 2 2 110 0.220 0.246
Median 1.000 3 3 49 0.098 0.082
Mode 1.000 4 4 7 0.014 0.015
Standard Deviation 0.998 5 2 0.004 0.002
Sample Variance 0.995 0.960 500 1 1
Kurtosis 0.291
Skewness 0.706
Range 5.000
Minimum 0.000
Maximum 5.000
Sum 615.000
Count 500.000
Poisson (μ=3)
(by 1)
Poisson Population Bin Bin Frequency Rel. Freq Population
0 0 23 0.046 0.050
Mean 3.060 3.000 1 1 71 0.142 0.149
Standard Error 0.079 2 2 109 0.218 0.224
Median 3.000 3 3 114 0.228 0.224
Mode 3.000 4 4 95 0.19 0.168
Standard Deviation 1.757 5 5 43 0.086 0.101
Sample Variance 3.087 3.000 6 6 23 0.046 0.050
Kurtosis 0.510 7 22 0.044 0.034
Skewness 0.647 500 1 1
Range 9.000
Minimum 0.000
Maximum 9.000
Sum 1530.000
Count 500.000
C. Uniform (a=30 b=100)
(by 10)
C. Uniform Population Bin Bin Frequency Rel. Freq Population
40 30-40 52 0.104 0.143
Mean 65.982 65 50 40-50 83 0.166 0.143
Standard Error 0.881 60 50-60 65 0.13 0.143
Median 66.423 70 60-70 80 0.16 0.143
Mode 50.404 80 70-80 76 0.152 0.143
Standard Deviation 19.695 90 80-90 68 0.136 0.143
Sample Variance 387.900 408.333 90-100 76 0.152 0.143
Kurtosis -1.174 500 1.000 1.000
Skewness -0.012
Range 69.421
Minimum 30.551
Maximum 99.972
Sum 32990.795
Count 500.000
Normal (μ=50 σ=5)
(by 5)
Normal Population Bin Bin Frequency Rel. Freq Population
40 35-40 7 0.014 0.023
Mean 50.293 50 45 40-45 53 0.106 0.136
Standard Error 0.213 50 45-50 177 0.354 0.341
Median 50.255 55 50-55 182 0.364 0.341
Mode 47.255 60 55-60 70 0.140 0.136
Standard Deviation 4.755 65 60-65 10 0.020 0.021
Sample Variance 22.614 25 65-70 1 0.002 0.001
Kurtosis -0.062 500 1.000 1
Skewness 0.125
Range 28.849
Minimum 37.926
Maximum 66.775
Sum 25146.664
Count 500.000
Exponential (μ=1/3)
(by .4)
Exponential Population Bin Bin Frequency Rel. Freq Population
0.4 0.0-0.4 355 0.710 0.699
Mean 0.305 0.333 0.8 0.4-0.8 114 0.228 0.210
Standard Error 0.013 1.2 0.8-1.2 23 0.046 0.063
Median 0.218 1.6 1.2-1.6 7 0.014 0.019
Mode 0.411 2 1.6-2.0 1 0.002 0.006
Standard Deviation 0.287 2.4 2.0-2.4 0 0.000 0.002
Sample Variance 0.082 0.111 2.4-2.8 0 0.000 0.001
Kurtosis 3.342 500 1.000 1.000
Skewness 1.654
Range 1.615
Minimum 0.000
Maximum 1.615
Sum 152.679
Count 500.000
Central Limit Theorem
Coin Flip Set 1 Set 2 Set 3 Set 4 Set 5 Set 6 Set 7 Set 8 Set 9 Set 10 Set 11 Set 12 Set 13 Set 14 Set 15 Set 16 Set 17 Set 18 Set 19 Set 20 Set 21 Set 22 Set 23 Set 24 Set 25 Set 26 Set 27 Set 28 Set 29 Set 30 Set 31 Set 32 Set 33 Set 34 Set 35 Set 36 Set 37 Set 38 Set 39 Set 40 Set 41 Set 42 Set 43 Set 44 Set 45 Set 46 Set 47 Set 48 Set 49 Set 50 Set 51 Set 52 Set 53 Set 54 Set 55 Set 56 Set 57 Set 58 Set 59 Set 60 Set 61 Set 62 Set 63 Set 64 Set 65 Set 66 Set 67 Set 68 Set 69 Set 70 Set 71 Set 72 Set 73 Set 74 Set 75 Set 76 Set 77 Set 78 Set 79 Set 80 Set 81 Set 82 Set 83 Set 84 Set 85 Set 86 Set 87 Set 88 Set 89 Set 90 Set 91 Set 92 Set 93 Set 94 Set 95 Set 96 Set 97 Set 98 Set 99 Set 100 Set 101 Set 102 Set 103 Set 104 Set 105 Set 106 Set 107 Set 108 Set 109 Set 110 Set 111 Set 112 Set 113 Set 114 Set 115 Set 116 Set 117 Set 118 Set 119 Set 120 Set 121 Set 122 Set 123 Set 124 Set 125 Set 126 Set 127 Set 128 Set 129 Set 130 Set 131 Set 132 Set 133 Set 134 Set 135 Set 136 Set 137 Set 138 Set 139 Set 140 Set 141 Set 142 Set 143 Set 144 Set 145 Set 146 Set 147 Set 148 Set 149 Set 150 Set 151 Set 152 Set 153 Set 154 Set 155 Set 156 Set 157 Set 158 Set 159 Set 160 Set 161 Set 162 Set 163 Set 164 Set 165 Set 166 Set 167 Set 168 Set 169 Set 170 Set 171 Set 172 Set 173 Set 174 Set 175 Set 176 Set 177 Set 178 Set 179 Set 180 Set 181 Set 182 Set 183 Set 184 Set 185 Set 186 Set 187 Set 188 Set 189 Set 190 Set 191 Set 192 Set 193 Set 194 Set 195 Set 196 Set 197 Set 198 Set 199 Set 200 Set 201 Set 202 Set 203 Set 204 Set 205 Set 206 Set 207 Set 208 Set 209 Set 210 Set 211 Set 212 Set 213 Set 214 Set 215 Set 216 Set 217 Set 218 Set 219 Set 220 Set 221 Set 222 Set 223 Set 224 Set 225 Set 226 Set 227 Set 228 Set 229 Set 230 Set 231 Set 232 Set 233 Set 234 Set 235 Set 236 Set 237 Set 238 Set 239 Set 240 Set 241 Set 242 Set 243 Set 244 Set 245 Set 246 Set 247 Set 248 Set 249 Set 250 Set 251 Set 252 Set 253 Set 254 Set 255 Set 256 Set 257 Set 258 Set 259 Set 260 Set 261 Set 262 Set 263 Set 264 Set 265 Set 266 Set 267 Set 268 Set 269 Set 270 Set 271 Set 272 Set 273 Set 274 Set 275 Set 276 Set 277 Set 278 Set 279 Set 280 Set 281 Set 282 Set 283 Set 284 Set 285 Set 286 Set 287 Set 288 Set 289 Set 290 Set 291 Set 292 Set 293 Set 294 Set 295 Set 296 Set 297 Set 298 Set 299 Set 300
1 Head Head Tail Tail Head Head Head Head Head Head Tail Tail Tail Tail Head Head Tail Head Tail Head Tail Tail Tail Head Head Head Head Tail Head Tail Tail Tail Head Tail Tail Tail Tail Head Tail Head Head Head Head Tail Head Head Head Head Head Head Head Tail Tail Head Tail Tail Head Tail Head Head Tail Tail Head Head Head Head Tail Head Head Tail Tail Tail Head Tail Head Tail Head Head Head Head Tail Head Head Head Tail Tail Tail Tail Tail Head Head Head Tail Tail Tail Head Head Head Tail Head Head Head Tail Head Head Tail Head Tail Head Head Tail Tail Head Tail Head Head Tail Tail Tail Head Tail Tail Tail Head Tail Head Tail Head Head Tail Tail Tail Head Tail Head Head Head Head Head Tail Head Tail Tail Tail Head Tail Tail Tail Tail Tail Tail Head Tail Tail Head Tail Head Head Head Head Tail Tail Tail Head Tail Tail Head Head Head Head Head Tail Tail Tail Tail Tail Head Head Tail Tail Head Head Tail Head Tail Head Tail Tail Head Tail Head Tail Head Head Head Head Tail Tail Head Head Tail Head Tail Head Tail Tail Tail Head Tail Head Head Tail Head Head Tail Tail Tail Tail Tail Head Head Tail Tail Tail Head Head Tail Tail Tail Head Head Head Tail Tail Tail Head Head Head Head Tail Tail Head Head Tail Tail Tail Head Head Tail Tail Head Tail Head Tail Tail Head Tail Tail Tail Head Head Tail Tail Head Head Head Head Head Head Tail Head Head Head Head Head Head Tail Tail Tail Head Tail Head Tail Head Tail Head Tail Head Tail Tail Head Tail Tail Head Tail Tail Head Head Head Head
2 Tail Head Tail Head Tail Head Tail Tail Tail Tail Head Head Tail Tail Tail Head Tail Tail Tail Head Head Tail Tail Head Tail Head Head Tail Tail Tail Tail Head Tail Tail Tail Head Head Tail Tail Tail Head Tail Tail Tail Head Head Tail Head Head Head Head Head Head Head Tail Tail Head Head Head Head Tail Tail Tail Head Head Tail Tail Tail Tail Head Head Tail Tail Tail Head Tail Head Tail Tail Tail Tail Head Tail Head Tail Tail Head Tail Tail Head Head Tail Head Tail Head Head Head Head Head Head Tail Tail Head Tail Head Head Tail Head Tail Head Head Tail Tail Tail Head Head Head Head Head Head Head Tail Tail Head Tail Tail Tail Tail Head Head Tail Head Head Tail Head Tail Tail Head Head Tail Tail Head Tail Head Head Tail Tail Tail Head Tail Head Head Head Tail Head Tail Head Tail Head Head Tail Tail Tail Tail Head Head Tail Head Tail Head Head Tail Head Tail Tail Head Tail Tail Head Head Head Tail Tail Tail Tail Head Tail Tail Tail Tail Head Head Head Tail Head Tail Head Head Head Tail Head Tail Head Head Tail Tail Head Head Tail Head Tail Head Head Head Head Tail Head Tail Head Tail Head Head Head Tail Tail Head Tail Head Tail Head Tail Tail Tail Tail Tail Tail Head Tail Head Tail Tail Head Tail Head Head Tail Head Tail Head Head Tail Head Tail Tail Tail Tail Tail Tail Tail Tail Head Head Head Tail Tail Tail Head Tail Tail Head Tail Tail Head Tail Tail Head Head Tail Tail Tail Head Head Head Head Head Tail Head Tail Head Tail Head Tail Head Head Head Head Tail Head Head Tail
3 Head Tail Head Tail Head Head Tail Tail Head Tail Head Tail Tail Head Tail Head Tail Head Head Head Tail Head Tail Head Head Tail Tail Head Tail Head Head Head Tail Head Tail Tail Tail Head Tail Tail Tail Tail Head Tail Head Tail Head Tail Tail Tail Tail Tail Head Head Tail Tail Tail Head Tail Tail Head Head Head Tail Tail Tail Head Head Tail Tail Head Head Head Head Head Head Tail Tail Head Head Head Tail Head Tail Head Head Tail Head Tail Head Tail Head Tail Tail Tail Tail Head Head Head Tail Tail Head Head Tail Tail Tail Head Tail Head Head Head Head Tail Tail Head Head Tail Head Head Head Tail Tail Tail Head Tail Head Head Head Head Head Head Head Tail Head Tail Tail Tail Tail Tail Tail Tail Tail Head Head Head Head Head Head Tail Tail Head Tail Head Head Head Head Tail Tail Tail Head Head Tail Tail Head Tail Head Tail Head Head Head Tail Head Tail Head Tail Head Tail Head Tail Head Tail Head Head Head Tail Tail Head Head Tail Head Tail Tail Tail Tail Tail Head Tail Head Tail Tail Tail Head Tail Head Head Tail Tail Tail Head Head Head Tail Tail Tail Head Head Tail Head Head Head Head Head Head Head Tail Head Head Tail Tail Tail Tail Head Head Tail Tail Tail Tail Head Head Head Tail Head Tail Tail Tail Head Tail Head Tail Head Tail Tail Head Head Tail Tail Head Head Tail Head Tail Tail Tail Head Head Head Head Head Tail Tail Head Head Head Tail Tail Tail Head Tail Head Head Head Head Head Head Tail Tail Tail Tail Tail Tail Head Head Tail Head Head Head Tail Tail Tail Head
4 Head Tail Tail Head Tail Tail Tail Tail Head Head Head Tail Head Tail Tail Head Tail Tail Tail Head Head Tail Tail Tail Head Head Tail Head Head Head Tail Head Head Tail Head Head Tail Head Tail Tail Tail Head Tail Head Head Head Tail Head Head Tail Head Head Head Tail Tail Head Head Head Tail Head Head Tail Head Head Head Head Tail Tail Tail Tail Head Tail Tail Tail Tail Head Head Head Head Head Head Head Head Head Tail Tail Head Tail Head Tail Tail Tail Tail Head Tail Tail Tail Tail Head Head Tail Tail Tail Tail Tail Tail Head Head Tail Tail Tail Head Tail Tail Head Tail Tail Tail Head Tail Tail Head Head Head Tail Head Tail Head Head Head Head Head Tail Head Tail Tail Tail Head Tail Tail Tail Tail Tail Tail Tail Head Tail Tail Head Tail Head Head Tail Head Tail Head Tail Tail Head Tail Head Tail Tail Head Tail Head Head Head Tail Head Head Head Head Head Head Head Head Head Head Tail Head Head Head Tail Tail Head Head Tail Head Head Head Tail Tail Head Head Head Tail Tail Head Head Tail Head Tail Tail Tail Head Head Tail Head Head Head Tail Head Tail Tail Tail Tail Head Head Head Head Tail Tail Tail Head Tail Head Head Head Tail Tail Tail Tail Head Head Head Head Head Head Head Head Head Tail Head Tail Head Tail Head Tail Head Head Tail Head Tail Head Head Tail Head Head Head Tail Head Tail Head Head Head Head Head Tail Tail Head Tail Head Tail Head Tail Head Tail Tail Head Tail Head Tail Tail Head Head Tail Tail Tail Head Tail Head Tail Tail Tail Head Tail Tail Head Tail
5 Head Tail Tail Head Head Tail Tail Head Tail Head Head Tail Head Tail Head Tail Head Tail Head Tail Head Head Tail Tail Tail Head Head Tail Head Tail Head Tail Head Head Tail Head Head Head Tail Tail Tail Tail Head Head Tail Tail Tail Head Tail Head Tail Head Tail Head Head Head Tail Tail Head Head Tail Tail Tail Head Head Tail Tail Head Head Head Head Head Head Head Tail Tail Head Head Tail Head Head Tail Tail Head Head Head Head Head Head Head Head Head Tail Tail Tail Head Tail Tail Tail Head Tail Tail Tail Tail Head Head Tail Head Head Head Head Head Tail Head Tail Head Tail Head Tail Head Tail Head Tail Head Tail Head Tail Tail Tail Head Head Tail Tail Head Head Head Tail Tail Tail Head Tail Head Tail Tail Tail Head Tail Head Tail Head Head Tail Head Tail Head Head Tail Tail Tail Tail Head Tail Head Tail Tail Head Head Tail Head Head Tail Head Tail Tail Tail Tail Head Tail Head Tail Head Head Head Tail Tail Tail Head Tail Head Tail Tail Tail Head Tail Tail Head Tail Tail Head Tail Head Head Head Tail Tail Head Tail Tail Tail Head Tail Tail Head Tail Head Head Tail Tail Head Tail Head Tail Head Head Tail Head Tail Head Head Tail Head Head Head Tail Tail Head Head Tail Tail Tail Tail Head Tail Tail Head Tail Head Head Tail Tail Head Head Tail Tail Head Head Head Head Tail Head Head Tail Tail Head Head Tail Tail Tail Head Tail Tail Tail Tail Tail Tail Head Head Tail Head Tail Tail Head Head Tail Head Head Tail Head Head Tail Head Tail Tail Head Head Head Tail Head Head Tail
6 Head Head Head Head Head Tail Head Tail Tail Head Head Head Head Tail Head Head Tail Tail Head Head Tail Tail Tail Tail Tail Head Tail Tail Tail Tail Tail Tail Tail Tail Head Head Tail Head Head Tail Head Head Head Tail Head Head Head Tail Tail Tail Head Head Head Tail Head Tail Tail Tail Tail Head Tail Tail Head Head Head Head Tail Tail Tail Head Head Tail Tail Tail Tail Tail Head Tail Head Tail Tail Head Tail Tail Head Head Head Tail Tail Head Tail Head Head Head Head Head Tail Tail Tail Tail Head Tail Head Tail Head Tail Tail Head Head Tail Tail Tail Head Tail Tail Tail Head Head Tail Tail Tail Head Tail Head Tail Head Head Head Tail Tail Tail Head Head Head Head Tail Head Head Tail Head Tail Head Head Tail Tail Tail Head Head Head Tail Tail Tail Head Head Tail Head Head Tail Tail Tail Head Tail Head Tail Head Tail Tail Head Tail Head Tail Head Tail Tail Head Tail Head Head Head Head Head Tail Head Tail Tail Tail Tail Tail Head Tail Head Head Tail Head Tail Tail Head Tail Head Tail Head Tail Head Head Head Head Head Tail Tail Tail Head Head Head Head Tail Head Tail Tail Head Head Tail Head Tail Head Tail Tail Tail Tail Tail Tail Tail Head Head Head Head Head Head Tail Head Head Head Tail Head Tail Tail Tail Tail Tail Head Tail Head Head Head Head Head Tail Head Tail Head Tail Tail Head Tail Tail Tail Head Tail Head Tail Head Head Head Head Tail Tail Tail Tail Tail Tail Head Head Tail Head Tail Tail Tail Head Tail Head Head Tail Head Tail Tail Head Head Head Tail Head Tail
7 Tail Tail Head Head Head Head Head Tail Tail Tail Tail Tail Tail Head Head Head Tail Tail Tail Head Head Head Head Tail Head Tail Tail Tail Tail Tail Tail Tail Head Tail Head Head Tail Tail Head Head Tail Tail Head Head Tail Tail Head Head Head Tail Head Head Tail Head Tail Head Head Head Tail Tail Head Head Tail Head Head Head Tail Tail Head Tail Head Head Tail Tail Tail Head Head Tail Head Head Tail Head Head Tail Tail Tail Tail Head Head Tail Tail Head Head Head Tail Tail Head Tail Tail Head Tail Head Tail Head Tail Head Tail Head Head Tail Head Tail Head Tail Head Head Tail Tail Head Tail Head Tail Tail Head Head Head Head Head Head Head Tail Head Head Head Head Tail Tail Tail Tail Tail Head Head Tail Head Head Head Tail Tail Head Head Tail Head Tail Head Tail Head Tail Tail Tail Head Tail Head Tail Tail Head Tail Tail Tail Head Tail Head Tail Tail Tail Head Head Tail Head Tail Tail Head Tail Head Head Tail Tail Head Head Head Tail Head Tail Tail Head Head Tail Tail Head Head Tail Tail Head Tail Tail Tail Tail Tail Tail Head Tail Tail Head Head Tail Tail Tail Tail Tail Tail Tail Tail Tail Tail Tail Head Tail Tail Tail Head Tail Head Tail Tail Tail Tail Tail Head Head Tail Tail Tail Tail Head Tail Tail Tail Head Head Head Tail Head Tail Tail Head Tail Tail Head Head Head Tail Tail Head Head Tail Tail Tail Tail Head Head Head Tail Head Head Tail Tail Tail Head Head Head Tail Head Tail Tail Head Tail Tail Tail Tail Tail Tail Tail Tail Head Tail Tail Tail Head Head Tail Head
8 Head Head Tail Tail Tail Tail Tail Head Tail Head Tail Head Tail Head Tail Tail Tail Tail Tail Tail Head Head Head Tail Tail Head Tail Head Tail Head Tail Head Tail Head Tail Tail Head Tail Tail Head Head Tail Head Tail Head Head Tail Head Head Tail Tail Head Tail Tail Head Head Tail Tail Tail Head Head Tail Head Head Tail Head Tail Tail Tail Tail Tail Head Tail Head Head Tail Head Tail Tail Tail Head Tail Head Tail Tail Tail Tail Tail Tail Tail Tail Tail Head Head Tail Tail Tail Head Tail Head Head Tail Head Tail Head Tail Tail Tail Tail Tail Tail Head Head Tail Tail Head Tail Head Head Tail Tail Head Head Head Head Head Tail Tail Head Tail Head Tail Head Head Head Head Head Head Head Head Tail Tail Head Head Head Head Tail Head Tail Tail Head Head Head Head Tail Head Head Head Tail Tail Head Tail Tail Tail Head Tail Head Tail Head Tail Head Tail Head Tail Head Tail Head Tail Head Head Tail Head Tail Tail Tail Tail Head Head Tail Head Tail Head Head Head Head Tail Head Head Tail Head Tail Head Head Tail Head Head Head Head Tail Head Tail Head Head Tail Tail Tail Tail Tail Head Head Head Tail Tail Tail Tail Tail Tail Head Head Head Tail Tail Tail Tail Head Tail Head Head Head Tail Head Tail Head Head Tail Head Tail Tail Head Head Head Head Tail Head Head Head Head Head Head Tail Tail Tail Tail Tail Head Tail Tail Tail Tail Tail Tail Head Tail Head Head Head Tail Tail Tail Head Head Head Head Head Tail Head Tail Head Tail Head Tail Head Head Tail Head Head Head Tail Tail Head
9 Head Tail Tail Head Tail Tail Head Tail Head Tail Head Tail Head Head Head Tail Tail Tail Head Head Tail Head Head Head Tail Head Head Head Head Head Tail Head Tail Tail Head Head Tail Head Tail Tail Head Tail Head Tail Head Tail Tail Tail Head Head Head Head Head Head Head Tail Tail Head Head Head Tail Head Head Head Head Head Tail Head Tail Tail Head Head Head Tail Head Head Tail Tail Tail Tail Head Tail Head Tail Tail Head Head Tail Head Tail Head Head Tail Head Tail Head Tail Tail Head Head Head Head Head Head Tail Head Tail Tail Head Head Head Head Head Head Head Tail Head Tail Head Tail Tail Tail Tail Head Head Head Tail Head Tail Tail Head Tail Head Head Tail Head Head Head Tail Tail Tail Head Head Tail Head Head Tail Tail Tail Tail Tail Head Tail Tail Head Tail Head Tail Tail Tail Tail Tail Tail Head Head Head Tail Head Head Tail Head Head Tail Head Head Tail Tail Tail Tail Head Tail Head Head Head Head Tail Tail Head Tail Head Head Head Head Tail Tail Head Tail Tail Tail Head Head Tail Head Tail Tail Head Tail Tail Head Head Head Tail Head Head Tail Head Tail Tail Head Tail Head Head Tail Head Tail Tail Head Head Head Tail Head Head Tail Tail Head Head Head Tail Head Tail Tail Tail Head Tail Tail Tail Head Tail Tail Tail Tail Tail Head Tail Tail Tail Tail Tail Head Tail Tail Head Tail Tail Tail Head Tail Tail Tail Tail Head Head Tail Head Tail Head Tail Tail Tail Tail Head Tail Tail Tail Tail Head Tail Tail Head Tail Tail Head Head Head Tail Head Tail Tail Head Head
10 Tail Head Head Head Tail Tail Tail Head Tail Head Tail Tail Head Head Head Tail Tail Head Tail Head Tail Head Head Head Head Head Head Head Tail Head Head Head Tail Head Head Head Tail Head Tail Head Tail Head Head Head Head Tail Tail Tail Head Head Tail Tail Tail Head Head Head Head Head Head Head Head Tail Tail Tail Head Tail Tail Head Head Tail Tail Tail Head Tail Tail Head Tail Tail Tail Tail Head Tail Head Tail Tail Head Tail Head Head Tail Head Head Tail Head Head Head Tail Tail Head Head Tail Head Head Tail Head Head Head Head Head Head Tail Tail Head Tail Tail Tail Tail Tail Head Head Tail Head Tail Tail Head Tail Head Tail Tail Head Head Head Tail Tail Tail Tail Head Tail Tail Head Head Head Head Tail Head Tail Tail Tail Tail Head Head Head Head Tail Head Tail Head Tail Tail Head Tail Head Tail Head Tail Head Head Head Tail Tail Head Tail Head Tail Tail Tail Head Head Head Head Head Head Head Tail Head Head Tail Tail Head Tail Tail Head Head Head Head Head Tail Head Head Tail Tail Head Tail Tail Head Tail Head Tail Head Head Head Tail Tail Head Tail Tail Tail Head Tail Tail Head Head Tail Head Tail Tail Tail Tail Head Head Head Tail Head Tail Tail Tail Head Head Head Head Head Head Head Tail Tail Tail Head Tail Head Head Head Head Tail Head Tail Tail Tail Head Head Tail Tail Tail Tail Head Tail Head Tail Head Head Head Tail Head Head Tail Tail Head Tail Tail Tail Head Head Tail Tail Head Tail Tail Tail Tail Tail Tail Tail Tail Tail Tail Tail Tail Head Tail Tail Tail
Proportion Heads: 0.7 0.5 0.4 0.7 0.5 0.4 0.4 0.4 0.4 0.6 0.6 0.3 0.5 0.5 0.6 0.6 0.1 0.3 0.4 0.8 0.5 0.6 0.4 0.5 0.5 0.8 0.5 0.5 0.4 0.5 0.3 0.6 0.4 0.4 0.5 0.7 0.3 0.7 0.2 0.4 0.5 0.4 0.8 0.4 0.8 0.5 0.4 0.6 0.7 0.5 0.6 0.7 0.5 0.7 0.5 0.5 0.5 0.6 0.5 0.8 0.5 0.3 0.6 0.8 0.8 0.6 0.1 0.5 0.4 0.3 0.7 0.5 0.5 0.3 0.5 0.5 0.7 0.3 0.5 0.5 0.6 0.5 0.7 0.4 0.3 0.5 0.5 0.4 0.5 0.5 0.5 0.7 0.4 0.6 0.3 0.6 0.4 0.4 0.5 0.8 0.4 0.5 0.6 0.3 0.6 0.5 0.4 0.6 0.7 0.6 0.5 0.5 0.6 0.2 0.6 0.6 0.3 0.5 0.7 0.5 0.2 0.5 0.2 0.9 0.4 0.8 0.4 0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.6 0.4 0.5 0.6 0.3 0.4 0.3 0.6 0.5 0.4 0.7 0.6 0.2 0.4 0.4 0.3 0.6 0.7 0.6 0.5 0.6 0.6 0.6 0.2 0.3 0.5 0.5 0.2 0.2 0.5 0.5 0.6 0.5 0.7 0.6 0.6 0.7 0.5 0.4 0.3 0.5 0.4 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.4 0.2 0.4 0.5 0.4 0.6 0.4 0.6 0.5 0.6 0.6 0.6 0.6 0.3 0.5 0.7 0.4 0.4 0.7 0.5 0.4 0.4 0.5 0.5 0.3 0.5 0.8 0.6 0.4 0.8 0.5 0.3 0.4 0.1 0.3 0.7 0.5 0.8 0.5 0.3 0.5 0.3 0.4 0.3 0.5 0.6 0.4 0.5 0.5 0.4 0.2 0.4 0.5 0.9 0.6 0.8 0.4 0.4 0.6 0.6 0.3 0.2 0.3 0.6 0.5 0.5 0.5 0.7 0.5 0.5 0.5 0.4 0.4 0.5 0.6 0.6 0.4 0.3 0.5 0.2 0.5 0.5 0.6 0.4 0.6 0.4 0.4 0.5 0.7 0.7 0.3 0.3 0.6 0.5 0.1 0.3 0.6 0.7 0.6 0.5 0.6 0.3 0.5 0.2 0.3 0.4 0.3 0.4 0.5 0.4 0.5 0.5 0.7 0.5 0.4 0.6 0.5
Proportion Heads Proportion Probability
Sample Population Heads Frequency Sample Population
Mean 0.497 0.500 0.0 0 0.000 0.002
Variance 0.023 0.025 0.1 4 0.013 0.011
0.2 13 0.043 0.043
0.3 33 0.110 0.114
0.4 57 0.190 0.205
0.5 85 0.283 0.248
0.6 64 0.213 0.205
0.7 29 0.097 0.114
0.8 13 0.043 0.043
0.9 2 0.007 0.011
1.0 0 0.000 0.002
300 1 1.000
Central Limit Theorem
Law of Large Numbers: as the number of sets (300) increases, the sample curve approaches the population curve.
Central Limit Theorem: as the number of coin flips (10) increases, the curves become more bell-shaped.

&"Calibri,Italic"&A

D.Uniform(k=8)

Sample

1 2 3 4 5 6 7 More 0.124 0.122 0.108 0.12 0.13200000000000001 0.114 0.13200000000000001 0.14799999999999999 Population

1 2 3 4 5 6 7 More 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125

Bernoulli(p=0.2)

Sample

0 1 0.82199999999999995 0.17799999999999999 Population 0 1 0.8 0.19999999999999996

Binomial (p=0.2)

Sample

0.24399999999999999 0.42 0.22 9.8000000000000004E-2 1.4E-2 4.0000000000000001E-3 Population

0.26214399999999993 0.39321600000000001 0.24575999999999998 8.1920000000000021E-2 1.5359999999999997E-2 1.6000000000000458E-3

Binomial (p=0.2)

4.5999999999999999E-2 0.14199999999999999 0.218 0.22800000000000001 0.19 8.5999999999999993E-2 4.5999999999999999E-2 4.3999999999999997E-2 4.9787068367863944E-2 0.14936120510359185 0.22404180765538775 0.22404180765538778 0.16803135574154085 0.10081881344492449 5.0409406722462261E-2 3.3508535308841125E-2

C. Uniform(a=30,b=100)

Sample

30-40 40-50 50-60 60-70 70-80 80-90 90-100 0.104 0.16600000000000001 0.13 0.16 0.152 0.13600000000000001 0.152 Population

30-40 40-50 50-60 60-70 70-80 80-90 90-100 0.14285714285714285 0.14285714285714285 0.14285714285714285 0.14285714285714285 0.14285714285714285 0.14285714285714285 0.14285714285714285

Normal(μ, σ =5)

Sample

35-40 40-45 45-50 50-55 55-60 60-65 65-70 1.4E-2 0.106 0.35399999999999998 0.36399999999999999 0.14000000000000001 0.02 2E-3 Population

35-40 40-45 45-50 50-55 55-60 60-65 65-70 2.2750131948179191E-2 0.13590512198327781 0.34134474606854304 0.34134474606854304 0.13590512198327775 2.1400233916549105E-2 1.3498980316301035E-3

Exponential(λ=1/3)

Sample

0.0-0.4 0.4-0.8 0.8-1.2 1.2-1.6 1.6-2.0 2.0-2.4 2.4-2.8 0.71 0.22800000000000001 4.5999999999999999E-2 1.4E-2 2E-3 0 0 Population

0.0-0.4 0.4-0.8 0.8-1.2 1.2-1.6 1.6-2.0 2.0-2.4 2.4-2.8 0.69880578808779803 0.21047625862278951 6.3394230842119925E-2 1.9093975398272511E-2 5.750994872353643E-3 1.732166368289656E-3 7.4658580837672073E-4

Distribution of proprtion of heads in 300 sets of 10 coin flips

Sample 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 1.3333333333333334E-2 4.3333333333333335E-2 0.11 0.19 0.28333333333333333 0.21333333333333335 9.6666666666666665E-2 4.3333333333333335E-2 6.6666666666666671E-3 0 Population 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 2.2132629289599122E-3 1.1215084824802293E-2 4.3494801249566804E-2 0.11446770657062669 0.20452396144896892 0.24817036595415087 0.20452396144896878 0.11446770657062666 4.3494801249566839E-2 1.1215084824802268E-2 2.2132629289599581E-3

Proportion of heads

Probability

Inferential Statistics

Data
Executive Salary Gender Education Pay PayD Salary2
1 79 Female Bachelors 81
2 76 Female Associates 75
3 83 Male Masters 88
4 92 Male Masters 95
5 80 Female Bachelors 83
6 81 Female Masters 84
7 77 Male Masters 82
8 87 Male Masters 90
9 69 Male Bachelors 81
10 70 Female Bachelors 71
11 73 Male Associates 79
12 80 Male Associates 73
13 81 Female Associates 78
14 87 Male Masters 88
15 78 Female Associates 78
16 78 Female Masters 80
17 77 Male Masters 88
18 81 Male Bachelors 86
19 75 Female Associates 69
20 83 Male Bachelors 79
21 74 Female Bachelors 77
22 85 Male Masters 89
23 86 Male Bachelors 93
24 73 Female Associates 79
25 70 Male Associates 76
26 81 Female Bachelors 75
27 77 Male Bachelors 81
28 85 Male Associates 81
29 69 Female Associates 66
30 73 Female Associates 78
31 91 Male Masters 93
32 75 Male Bachelors 75
33 90 Male Masters 87
34 74 Female Bachelors 70
35 72 Female Bachelors 73
Salary
Variable: Salary (Normal)
One Population: All Executives
Unknown variance so use the t distribution; if variance is known use the z distribution.
Two Populations: Male Executives vs. Female Executives
Unknown variances so use the t distribution; if variances are known use the z distribution.
If variances are assumed unequal use the SE with the special DF. If variances are assumed equal use the SE (P) with the regular DF.
Gender Gender
All Male Female Difference in Means
N Standard Error
Mean Special DF 29.520 - Use ROUND function with 0 digits.
Variance Pooled Variance
Standard Error Standard Error (P)
DF Regular DF
Confidence Intervals
One Population Confid. Alpha DF Mean SE Critical t MOE Lower CL Upper CL
90% 0.10
95% 0.05
99% 0.01
Two Populations Confid. Alpha DF Δ Means SE Critical t MOE Lower CL Upper CL
(Unequal Variances) 90% 0.10
95% 0.05
99% 0.01
Two Populations Confid. Alpha DF Δ Means SE Critical t MOE Lower CL Upper CL
(Equal Variances) 90% 0.10
95% 0.05
99% 0.01
Hypothesis Tests
One Population Null Hypothesis Alpha DF Mean SE t-statistic L Critical t U Critical t P-value Decision
μ ≥ 77 0.10
μ ≤ 77 0.10
μ = 77 0.10
μ ≥ 77 0.05
μ ≤ 77 0.05
μ = 77 0.05
μ ≥ 77 0.01
μ ≤ 77 0.01
μ = 77 0.01
Hypothesis Tests
Two Populations Null Hypothesis Alpha DF Δ Means SE t-statistic L Critical t U Critical t P-value Decision
(Unequal Variances) μM - μF ≥ 8 0.10
μM - μF ≤ 8 0.10
μM - μF = 8 0.10
μM - μF ≥ 8 0.05
μM - μF ≤ 8 0.05
μM - μF = 8 0.05
μM - μF ≥ 8 0.01
μM - μF ≤ 8 0.01
μM - μF = 8 0.01
Two Populations Null Hypothesis Alpha DF Δ Means SE t-statistic L Critical t U Critical t P-value Decision
(Equal Variances) μM - μF ≥ 8 0.10
μM - μF ≤ 8 0.10
μM - μF = 8 0.10
μM - μF ≥ 8 0.05
μM - μF ≤ 8 0.05
μM - μF = 8 0.05
μM - μF ≥ 8 0.01
μM - μF ≤ 8 0.01
μM - μF = 8 0.01
Equivalent Two Population Hypothesis Tests
Salary
Male Female
Other Hypothesis Tests
Pay
Variable: PayD (Bernoulli)
One Population: All Executives
It must be that np ≥ 5 and n(1-p) ≥ 5. Use the z distribution.
For HT use the hypothesized value in calculating the SE.
Two Populations: Male Executives vs. Female Executives
It must be that np ≥ 5 and n(1-p) ≥ 5 for both populations. Use the z distribution.
For HT when the hypothesized value is 0, the variances are presumed equal so use the SE (P).
Gender Gender
All Male Female
N Difference in Props
Proportion Standard Error
Variance Pooled Variance
Standard Error Standard Error (P)
Confidence Intervals
One Population Confid. Alpha Proportion SE Critical z MOE Lower CL Upper CL
90% 0.10
95% 0.05
99% 0.01
Two Populations Confid. Alpha Δ Props SE Critical z MOE Lower CL Upper CL
90% 0.10
95% 0.05
99% 0.01
Hypothesis Tests
One Population Null Hypothesis Alpha Proportion SE z-statistic L Critical z U Critical z P-value Decision
p ≥ 0.50 0.10
p ≤ 0.50 0.10
p = 0.50 0.10
p ≥ 0.50 0.05
p ≤ 0.50 0.05
p = 0.50 0.05
p ≥ 0.50 0.01
p ≤ 0.50 0.01
p = 0.50 0.01
Hypothesis Tests
Two Populations Null Hypothesis Alpha Δ Props SE z-statistic L Critical z U Critical z P-value Decision
(Unequal Variances) pM - pF ≥ 0.15 0.10
pM - pF ≤ 0.15 0.10
pM - pF = 0.15 0.10
pM - pF ≥ 0.15 0.05
pM - pF ≤ 0.15 0.05
pM - pF = 0.15 0.05
pM - pF ≥ 0.15 0.01
pM - pF ≤ 0.15 0.01
pM - pF = 0.15 0.01
Two Populations Null Hypothesis Alpha Δ Props SE z-statistic L Critical z U Critical z P-value Decision
(Equal Variances) pM - pF ≥ 0 0.10
pM - pF ≤ 0 0.10
pM - pF = 0 0.10
pM - pF ≥ 0 0.05
pM - pF ≤ 0 0.05
pM - pF = 0 0.05
pM - pF ≥ 0 0.01
pM - pF ≤ 0 0.01
pM - pF = 0 0.01
Equivalent Two Population Hypothesis Tests
PayD
Male Female
Test of Independence
Test of Independence

&"Calibri,Italic"&A

Linear Modeling

Data
Executive Salary Age Gender Education Promotions AgeC GenD AgeC*GenD
1 79 49 Female Bachelors 4
2 76 38 Female Associates 0
3 83 60 Male Masters 4
4 92 63 Male Masters 6
5 80 55 Female Bachelors 3
6 81 54 Female Masters 6
7 77 42 Male Masters 4
8 87 59 Male Masters 6
9 69 42 Male Bachelors 1
10 70 36 Female Bachelors 1
11 73 48 Male Associates 2
12 80 53 Male Associates 2
13 81 46 Female Associates 2
14 87 57 Male Masters 4
15 78 49 Female Associates 1
16 78 40 Female Masters 2
17 77 55 Male Masters 4
18 81 48 Male Bachelors 5
19 75 42 Female Associates 1
20 83 52 Male Bachelors 3
21 74 41 Female Bachelors 2
22 85 62 Male Masters 3
23 86 53 Male Bachelors 5
24 73 36 Female Associates 0
25 70 44 Male Associates 2
26 81 50 Female Bachelors 3
27 77 50 Male Bachelors 3
28 85 60 Male Associates 3
29 69 39 Female Associates 0
30 73 48 Female Associates 2
31 91 59 Male Masters 5
32 75 44 Male Bachelors 3
33 90 64 Male Masters 5
34 74 42 Female Bachelors 0
35 72 46 Female Bachelors 1
Data (cont.)
AgeC Promotions AgeC*Promos GenD EducD1 EducD2 GenD*EducD1 GenD*EducD2
1. Salary by Age
2. Salary by Gender
Equivalent Two Population Hypothesis Tests
Salary
Male Female
3. Salary by Education
Equivalent Three Population Hypothesis Test
Salary
Associates Bachelors Masters
4. Salary by Promotions
5. Salary by Age, Gender
6. Salary by Age, Gender, Age*Gender
7. Salary by Age, Promotions
8. Salary by Age, Promotions, Age*Promotions
9. Salary by Gender, Education
10. Salary by Gender, Education, Gender*Education
Moving Average (Interval = 3)
Week Sales Forecast Squared Error
1 17
2 21
3 19
4 23
5 18
6 16
7 20
8 18
9 22
10 20
11 15
12 22
Exponential Smoothing (Optimized α)
Week Sales Forecast Squared Error
1 17
2 21
3 19
4 23
5 18
6 16
7 20
8 18
9 22
10 20
11 15
12 22
Multiplicative Model (Trend, Seasonal)
Moving Seasonal Seasonal Deseasonalized Squared
Quarter Sales Average Centered MA Irregular Value Index Sales Forecast Error
1 4.8
2 4.1
3 6.0
4 6.5
5 5.8
6 5.2
7 6.8
8 7.4
9 6.0
10 5.6
11 7.5
12 7.8
13 6.3
14 5.9
15 8.0
16 8.4
17
18
19
20
Multiplicative Model (Trend, Seasonal)
Year Quarter
2012 F
W
Sp
Su
2013 F
W
Sp
Su
2014 F
W
Sp
Su
2015 F
W
Sp
Su
2016 F
W
Sp
Su

&"Calibri,Italic"&A

Charts

Female 45.7%
Male 54.3%
Associates 31.4%
Bachelors 37.1%
Masters 31.4%
Low 60.0%
High 40.0%

Gender Bar Graph

Female Male 0.45714285714285713 0.54285714285714282

% Relative Frequency

Gender Pie Chart

Female Male 0.45714285714285713 0.54285714285714282

Female Male 0.45714285714285713 0.54285714285714282

Education Bar Graph

Associates Bachelors Masters 0.31428571428571428 0.37142857142857144 0.31428571428571428

% Relative Frequency

Education Pie Chart

Associates Bachelors Masters 0.31428571428571428 0.37142857142857144 0.31428571428571428

Pay Bar Graph

Low High 0.6 0.4

% Relative Frequency

Pay Pie Chart

Low High 0.6 0.4

Pivot

Count of Pay Column Labels
Row Labels High Low Grand Total
Associates 2 9 11
Bachelors 4 9 13
Masters 8 3 11
Grand Total 14 21 35