Stats

profilekatherinabe
HypothesisTest-Major1.xlsx
Home>Mathematics homework help>Statistics homework help>Stats

Z T

Small sample example Two-Tail Hypothesis example
Bag of seed scenario Two cities, Bradford and Kane are separated only by the Conewango River. There is competition between the two cities. The local paper recently reported that the mean household income in Bradford is $38,000 with a standard deviation of $6,000 for a sample of 40 households. The same article reported the mean income in Kane is $35,000 with a standard deviation of $7,000 for a sample of 35 households. At the .01 significance level can we conclude the mean income in Bradford is more? The processors of Fries’ Catsup indicate on the label that the bottle contains 16 ounces of catsup. The standard deviation of the process is 0.5 ounces. A sample of 36 bottles from last hour’s production revealed a mean weight of 16.12 ounces per bottle. At the .05 significance level is the process out of control? That is, can we conclude that the mean amount per bottle is different from 16 ounces?
A farmer maintains a database that records the weight of the bags of seeds he takes to market for sale.
Lately, he begins to suspect that his weight filling machine is off and that he feels that the bags are under filled.
He looks at his records and the average weight of each bag is 50 pounds. He examines a sample of 20 recent bags and weighs each of them. To his surprise, the average weight of the 20 sample bags is 49.13 pounds, with a standard deviation of 1.743. At the .05 level of significance, are the bags under filled.
Absenteeism scenario
An organization in the Pacific Northwest has been experiencing a high amount of absenteeism of their employees. The latest employee records showed that the average amount of absenteeism per week is 12 with a standard deviation of two. The CEO of the company thinks this is too high and wants something done to reduce the record of absenteeism. H0: µB £ µK ; H1: µB > µK
You meet with an action group from HR, and you recommend to the CEO to establish a flex time for employees to work. The CEO reluctantly agrees. a = 0.01 a = 0.05
t ==> Because both samples are more than 30, we can use z as the test statistic. t ==> Because sample are more than 30, we can use z as the test statistic.
After 49 weeks, the CEO notices that the average amount of absenteeism per week is now down to nine instead of the 12 in previous weeks. The CEO approaches you and ask if the flex time initiative has made a statistically significant difference. FDR The null hypothesis is rejected if z is greater than 2.33 FDR The null hypothesis is rejected if z is greater than 1.96 or if z is less than - 1.96
So, you conduct an eight-step statistical hypothesis test to determine the statistical significance of the effectiveness of flex time. What will be your recommendation? S S
Increase revenue scenario D decision is to not reject the null hypothesis. D decision is to not reject the null hypothesis.
the CEO of an advertising organization in San Francisco wants to increase revenue. So, he calls upon you as the vice president for operations to come up with some ideas that would increase revenue. C cannot conclude that the mean household income in Bradford is larger. C Machine is operating within specifications
The first action taken was to determine current revenue that the organization was making. You find out that the organization has been averaging approximately 75 (thousand) dollars per week with a standard deviation of 8000. R NTR R Don't fix something that isn't broken
After meeting with your group, you recommend to the CEO to increase advertising.
After 25 weeks, the CEO wants to know if advertising is made a statistically significant difference. You find out that the current revenue stream is now up to 80,000 week and you state to the CEO that yes, advertising has made a difference. The CEO wants a hypothesis tested at the .05 level of significance to determine if the company should continue advertising or try something else.

ANOVA

ANOVA Reject Ho if p < 0.05
Rosenbaum Restaurants specialize in meals for senior citizens. Katy Polsby, President, recently developed a new meat loaf dinner. Before making it a part of the regular menu she decides to test it in several of her restaurants. She would like to know if there is a difference in the mean number of dinners sold per day at the Anyor, Loris, and Lander restaurants. Use the .05 significance level.
Aynor Loris Lander
13 10 18 Ho: TIND Ha: TIAD
12 12 16 a = 0.05
14 13 17 t ANOVA - Three groups
12 11 17 FDR Reject Ho if Fvalue > Fcrv = 4.103
17
Statistics Fvalue = 39.103
Anova: Single Factor Decision Since Fvalue = 39.103 > Fcrv = 4.103, Reject Ho
SUMMARY Conclusion: TIAD
Groups Count Sum Average Variance Recommendation: Various
Aynor 4 51 12.75 0.917
Loris 4 46 11.5 1.667
Lander 5 85 17 0.5
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 76.25 2 38.125 39.103 0.000 4.103
Within Groups 9.75 10 0.975
Total 86 12
ANOVA TWO FACTOR
Employee Day Output Evening Output Night Output
McCartney 31 25 35
Neary 33 26 33
Schoen 28 24 30 F Distribution
Thompson 30 29 28 Skewed
Wagner 28 26 27 All Positive
Accept Reject Region
Anova: Two-Factor Without Replication Region Reject Ho if p < 0.05
SUMMARY Count Sum Average Variance Ho: TIND Ha: TIAD
McCartney 3 91 30.333 25.333 a = 0.05
Neary 3 92 30.667 16.333 t ANOVA - Three groups
Schoen 3 82 27.333 9.333 FDR Reject Ho if Fvalue > Fcrv = 4.103
Thompson 3 87 29 1
Wagner 3 81 27 1 Statistics Fvalue = 39.103
Decision Since Fvalue = 39.103 > Fcrv = 4.103, Reject Ho
Day Output 5 150 30 4.5 Conclusion: TIAD
Evening Output 5 130 26 3.5 Recommendation: Various Reject Ho if p < 0.05
Night Output 5 153 30.6 11.3
Ho: TIND Ha: TIAD
a = 0.05
ANOVA t ANOVA - Three groups
Source of Variation SS df MS F P-value F crit FDR Reject Ho if Fvalue > Fcrv = 4.103
Rows 33.733 4 8.433 1.552 0.276 3.838
Columns 62.533 2 31.267 5.755 0.028 4.459 Statistics Fvalue = 39.103
Error 43.467 8 5.433 Decision Since Fvalue = 39.103 > Fcrv = 4.103, Reject Ho
Conclusion: TIAD
Total 139.733 14 Recommendation: Various

Confidence Ints

Preliminary calculations from the data:
p = = .433 or 43.3%
n p = 60 * .50 = 30 > 5
n p = 60 * .50 = 30 > 5 CLT ==> z standard normal distribution distribution
p ± z = .433 ± 1.96 *
= .433 ± 0.1254 = ( .3076, .5584 ) Confidence Interval
Ho p ≤ .50 Ha p > .50
a = .05
test statistics CI for a population proportion
FDR Reject Ho if proportion in question is outside (not between) the two CI ( .3076 < p < .5584 )
Statistics
= (.3076, .5584 ) = Confidence Interval
Decision Cannot Reject Ho since .50 is in the interval
Conclusion: We cannot conclude that the use of debit cards is greater than .50
Recommendation: Various

Regression

Hypothesis testing: Does Advertising make a statistically significant difference in sales?
Advertisement ($'000) Sales ($'000) Regression Ho: TIND Ha: TIAD
1068 4489 SUMMARY OUTPUT a = 0.05
1026 5611 t ANOVA - Three groups
767 3290 Regression Statistics FDR Reject Ho if p < 0.05
885 4113 Multiple R 0.82
1156 4883 R Square 0.68 Statistics p = .98
1146 5425 Adjusted R Square 0.65 Decision Since p = .98 not less than 0.05, not enough evidence to reject Ho
892 4414 Standard Error 592.73 Conclusion: TIND
938 5506 Observations 12.00 Recommendation: Try something else. Advertising may not be most
769 3346 significant course of action.
677 3673 ANOVA
1184 6542 df SS MS F Significance F
1009 5088 Regression 1.00 7415845.78 7415845.78 21.11 0.00
Residual 10.00 3513330.88 351333.09
Total 11.00 10929176.67
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept -25.17 1042.26 -0.02 0.98 -2347.47 2297.13 -2347.47 2297.13
Advertisement ($'000) 4.92 1.07 4.59 0.00 2.53 7.31 2.53 7.31

Multiple Regression

Multiple Regression
Family Food Income Size Student
1 3900 376 4 0
2 5300 515 5 1 Ho: TIND Ha: TIAD
3 4300 516 4 0 a = 0.05
4 4900 468 5 0 t ANOVA - Three groups
5 6400 538 6 1 FDR Reject Ho if p < 0.05
6 7300 626 7 1
7 4900 543 5 0 Statistics p = .98
8 5300 437 4 0 Decision Since p = .98 not less than 0.05, not enough evidence to reject Ho
9 6100 608 5 1 Conclusion: TIND
10 6400 513 6 1 Recommendation: Try something else. Advertising may not be most
11 7400 493 6 1 significant course of action.
12 5800 563 5 0
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.8966614273
R Square 0.8040017151
Adjusted R Square 0.7305023583
Standard Error 572.6870553352
Observations 12 Income
(1) ---> Ho: TIND Ha: TIAD
ANOVA a = 0.05
df SS MS F Significance F t ANOVA - Three groups
Regression 3 10762902.96 3587634.32 10.94 0.00 FDR Reject Ho if p < 0.05
Residual 8 2623763.71 327970.46
Total 11 13386666.67 Statistics p = .74
Decision Since p = .74 not less than 0.05, not enough evidence to reject Ho, [no difference] ~ [not significant]
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Conclusion: TIND
Intercept 954.02 1580.84 0.60 0.56 -2691.40 4599.44 -2691.40 4599.44 Recommendation: The variable is not statistically significant.
(1) -- > Income 1.09 3.15 0.35 0.74 -6.18 8.36 -6.18 8.36
(2) -- > Size 748.38 302.95 2.47 0.04 49.77 1447.00 49.77 1447.00
(3) -- > Student 564.52 495.13 1.14 0.29 -577.26 1706.30 -577.26 1706.30
Size
(2) --> p = 0.04, statistically significant
student
(3) --> p =0.29, not statistically significant

Multiple Regression 2nd example

Square Feet Per Person Average Spending Sales Growth Over Previous Year (%) Loyalty Card % of Net Sales Annual Sales Per Sq Ft Median HH Income (3 Miles) Median Age (3 Miles) % w/ Bachelor's Degree (3 Miles) Variables Results
Obs SqFt Sales/Person SalesGrowth% LoyaltyCard% Sales/SqFt MedIncome MedAge BachDeg% Annual Sales
1 2354 6.81 -8.31 2.07 701.97 45177 34.4 31 1652437.4
2 2604 7.57 -4.01 2.54 209.93 51888 41.2 20 546657.7
3 2453 6.89 -3.94 1.66 364.92 51379 40.3 24 895148.8
4 2340 7.13 -3.39 2.06 443.04 66081 35.4 29 1036713.6
5 2500 7.04 -3.30 2.48 399.20 50999 31.5 18 998000.0
6 2806 6.93 -1.94 2.96 264.64 41562 36.3 30 742579.8
7 2250 7.11 -0.77 2.28 571.59 44196 35.1 14 1286077.5
8 2400 7.13 -0.37 2.34 642.25 50975 37.6 33 1541400.0
9 2709 6.58 -0.25 2.20 461.45 72808 34.9 28 1250068.1
10 1990 6.77 -0.17 2.34 638.82 79070 34.8 29 1271251.8
11 2392 6.66 0.47 2.09 484.38 78497 36.2 39 1158637.0
12 2408 7.03 0.55 2.47 581.09 41245 32.2 23 1399264.7
13 2627 7.03 0.77 2.04 267.71 33003 30.9 22 703274.2
14 2500 7.00 1.92 2.02 572.84 90988 37.7 37 1432100.0
15 1986 7.38 2.05 2.01 586.48 37950 34.3 24 1164749.3
16 2500 7.18 2.12 2.64 368.73 45206 32.4 17 921825.0
17 2668 7.35 2.84 2.22 351.47 79312 32.1 37 937722.0
18 2517 6.95 2.88 2.07 458.24 37345 31.4 22 1153390.1
19 1251 7.02 3.96 1.94 987.12 46226 30.4 36 1234887.1
20 2998 6.85 4.04 2.17 357.45 70024 33.9 34 1071635.1
21 2625 7.16 4.05 0.72 405.77 54982 35.6 26 1065146.3
22 2300 6.99 4.05 2.00 680.80 54932 35.9 20 1565840.0
23 2761 7.28 4.24 1.81 368.02 34097 33.6 20 1016103.2
24 2764 7.07 4.58 2.13 303.95 46593 37.9 26 840117.8
25 2430 7.05 5.09 2.50 393.90 51893 40.6 21 957177.0
26 2154 6.54 5.14 2.63 562.12 88162 37.7 37 1210806.5
27 2400 6.70 5.48 1.95 494.88 89016 36.4 34 1187712.0
28 2430 6.91 5.86 2.04 310.07 114353 40.9 34 753470.1
29 2549 7.58 5.91 1.41 373.46 75366 35.0 30 951949.5
30 2500 7.03 5.98 2.05 235.81 48163 26.4 16 589525.0
31 3653 6.84 6.08 2.13 413.08 49956 37.1 28 1508981.2
32 2440 6.94 6.08 2.08 625.22 45990 30.3 36 1525536.8
33 2600 7.07 6.13 2.73 274.30 45723 31.3 18 713180.0
34 2160 7.00 6.27 1.95 542.62 43800 29.6 36 1172059.2
35 2800 7.08 6.57 2.04 178.56 68711 32.9 18 499968.0
36 2757 6.75 6.90 1.62 375.33 65150 40.7 24 1034784.8
37 2450 6.81 6.94 1.95 329.09 39329 29.3 22 806270.5
38 2400 7.64 7.12 1.64 297.37 63657 37.3 29 713688.0
39 2270 6.62 7.39 1.78 323.17 67099 39.8 25 733595.9
40 2800 6.76 7.67 2.23 468.84 75151 33.9 28 1312752.0
41 2520 7.11 7.91 2.15 352.57 93876 35.0 40 888476.4
42 2487 7.05 8.08 2.83 380.34 79701 35.0 39 945905.6
43 2629 6.90 8.27 2.37 398.12 77115 35.9 30 1046657.5
44 3200 7.17 8.54 3.07 312.15 52766 33.0 17 998880.0
45 2335 6.75 8.58 2.19 452.16 32929 30.9 22 1055793.6
46 2500 7.45 8.72 1.28 698.64 87863 38.5 29 1746600.0
47 2449 7.00 8.75 1.76 367.19 73752 40.5 19 899248.3
48 2625 6.96 8.79 2.51 431.93 85366 32.1 29 1133816.3
49 3150 7.30 8.90 1.90 367.06 39180 34.8 18 1156239.0
50 2625 6.96 9.12 1.98 400.53 56077 38.0 19 1051391.3
51 2741 6.71 9.47 2.41 414.36 77449 37.0 34 1135760.8
52 2500 6.82 10.17 2.17 481.11 56822 34.7 25 1202775.0
53 2450 6.58 10.66 2.16 538.06 80470 36.4 30 1318247.0
54 2986 7.56 10.97 0.29 330.48 55584 36.8 21 986813.3
55 2967 6.98 11.34 1.85 249.93 78001 32.2 30 741542.3
56 3000 7.28 11.45 1.88 291.87 75307 34.8 30 875610.0
57 2500 6.76 11.51 2.19 517.40 76375 36.7 28 1293500.0
58 2600 6.92 11.73 2.56 551.58 61857 33.8 31 1434108.0
59 2800 6.73 11.83 2.16 386.81 61312 34.2 16 1083068.0
60 2986 6.91 11.95 2.10 427.50 72040 39.0 31 1276515.0
61 2223 6.77 12.47 1.98 453.94 92414 34.9 40 1009108.6
62 2300 7.33 12.80 0.87 512.46 92602 39.3 33 1178658.0
63 3799 7.87 13.78 1.07 345.27 59599 35.6 28 1311680.7
64 2700 6.95 14.09 3.38 234.04 72453 36.0 23 631908.0
65 2650 7.33 14.23 1.17 348.33 67925 41.1 16 923074.5
66 2500 6.95 14.60 2.14 348.47 42631 24.7 25 871175.0
67 2994 7.21 14.88 0.93 294.95 75652 40.5 25 883080.3
68 2718 7.25 15.42 2.22 361.14 39650 32.9 18 981578.5
69 3700 7.65 16.18 1.68 467.71 48033 30.3 15 1730527.0
70 2000 6.93 17.23 2.41 403.78 67403 36.2 19 807560.0
71 2400 6.79 18.43 2.81 245.74 80597 32.4 27 589776.0
72 2450 7.37 20.76 1.09 339.94 60928 43.5 21 832853.0
73 2575 6.76 25.54 0.64 400.82 73762 41.6 29 1032111.5
74 2400 7.97 28.81 1.77 326.54 64225 31.4 15 783696.0
SqFt Sales/Person SalesGrowth% LoyaltyCard% Sales/SqFt MedIncome MedAge BachDeg% Annual Sales
Mean 2580.472972973 7.0440540541 7.4140540541 2.0264864865 420.3054054054 62807.7027027027 35.2013513514 26.3108108108 1059381.31445946
Standard Error 43.5834521166 0.0345559009 0.7701092572 0.0642118026 15.9537705276 2081.3294543554 0.4248330606 0.8142851024 32598.5637174162
Median 2500 7 7.03 2.075 396.01 62757 35 26.5 1035749.205
Mode 2500 7.03 4.05 2.04 ERROR:#N/A ERROR:#N/A 34.8 29 ERROR:#N/A
Standard Deviation 374.9190313674 0.2972610997 6.6247303215 0.5523708116 137.2395233139 17904.2729542418 3.6545521714 7.0047453107 280423.448335629
Sample Variance 140564.280081451 0.0883641614 43.8870518327 0.3051135135 18834.6867594224 320562990.019993 13.3557515735 49.0664568678 78637310376.445
Kurtosis 3.7609207038 0.8543989501 1.1461660181 1.4536001998 2.8805131423 -0.5116060091 0.1638814936 -0.937297935 -0.1320716281
Skewness 0.5271708372 0.9036315033 0.4937474711 -0.7568911137 1.23589655 0.2978380118 -0.1669958223 0.1405441956 0.3614133314
Range 2548 1.43 37.12 3.09 808.56 81424 18.8 26 1246632
Minimum 1251 6.54 -8.31 0.29 178.56 32929 24.7 14 499968
Maximum 3799 7.97 28.81 3.38 987.12 114353 43.5 40 1746600
Sum 190955 521.26 548.64 149.96 31102.6 4647770 2604.9 1947 78394217.27
Count 74 74 74 74 74 74 74 74 74
5-number summary
Q0 1251 6.54 -8.31 0.29 178.56 32929 24.7 14 499968
Q1 2400 6.84 4.04 1.85 330.48 48033 32.4 20 875610
Q2 2500 7 7.255 2.075 396.01 63941 35 26.5 1035749.205
Q3 2749 7.175 11.48 2.31 482.745 76745 37.2 30.5 1222846.8
Q4 3799 7.97 28.81 3.38 987.12 114353 43.5 40 1746600
IQR 349 0.335 7.44 0.46 152.265 28712 4.8 10.5 347236.8

Sheet7

Sheet8

98.1

35

)000,7($

40

)000,6($

000,35$000,38$

22

z

44.1

365.0

00.1612.16

n

X

z