Stats analysis and a paper

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20160530201419chapter_8_procedures_v2.xlsx
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CI for mu with known sigma

CI of mu with known sigma or n>=30
Sample Size n 10
Estimate of mean xbar 488.5
Sample/population standard deviation sigma 10.543560436
Confidence Level c 0.95
Constant zc 1.9599639845
Stdev of Estimate sigma/sqrt(n) 3.3341665625
Margin of Error E=constant* Stdev of Estimate 6.534846381
CI Left Endpoint xbar-E 481.965153619
CI Right Endpoint xbar+E 495.034846381
Confidence Interval 481.965153619 ≤ μ ≤ 495.034846381

CI for mu unknown sigma

CI of mu with unknown sigma
Sample Size n 10 Brand X Brand Y Brand Z
Estimate xbar 488.5 501 410 488
Sample standard deviation s 10.543560436 475 398 467
Confidence Level c 0.95 495 391 483
Degree of Freedom df 9 490 412 484
Constant tc 2.2621571582 478 391 498
Stdev of Estimate sigma/sqrt(n) 3.3341665625 493 404 491
Margin of Error Constant*Stdev of Estimate 7.542408756 474 382 481
CI Left Endpoint xbar-E 480.957591244 481 411 502
CI Right Endpoint xbar+E 496.042408756 499 407 511
499 430 524
Avg (xbar) 488.5 403.6 492.9
Stdev (sigma) 10.543560436 13.704824779 16.4008807352
Confidence Interval 480.957591244 ≤ μ ≤ 496.042408756
This formula for a confidence interval for μ, the “true” process/population average

CI for proportion

CI for Proportion
Sample Size n 156
Successes x 12
Proportion of Successes phat 0.0769230769
Proportion of Failures qhat 0.9230769231
Confidence Level c 0.95
Constant zc 1.9599639845
Margin of Error E 0.0418150926
CI Left Endpoint phat-E 0.0351079844
CI Right Endpoint phat+E 0.1187381695
Confidence Interval 0.0351079844 ≤ π ≤ 0.1187381695

CI for Variance and STD

CI for Variance and Standard Deviation
Sample Size n 15 Brand X Brand Y Brand Z
Degree of Freedom df 14 501 410 488
Sample Standard Deviation s 1.02 475 398 467
Sample Variance s^2 1.0404 495 391 483
Confidence Level c 0.95 490 412 484
Right-Tail C.V. ChiR^2 26.1189480457 478 391 498
Left-Tail C.V. ChiL^2 5.6287261679 493 404 491
474 382 481
Variance CI Left Endpoint 0.5576641132 481 411 502
Variance CI Right Endpoint 2.5877258132 499 407 511
499 430 524
STD CI Left Endpoint 0.7467691164
STD CI Right Endpoint 1.6086409833 Avg (xbar) 488.5 403.6 492.9
Stdev (sigma) 10.543560436 13.704824779 16.4008807352
Variance Confidence Interval 0.5576641132 ≤ σ2 ≤ 2.5877258132
Stdev. Confidence Interval 0.7467691164 ≤ σ ≤ 1.6086409833

Prediction Int. for one observ.

Prediction Interval for one observation
Sample Size n 10 Brand X Brand Y Brand Z
Estimate xbar 488.5 501 410 488
Sample standard deviation s 10.543560436 475 398 467
Confidence Level c 0.95 495 391 483
Degree of Freedom df 9 490 412 484
Constant tc 2.2621571582 478 391 498
Stdev of Estimate sigma/sqrt(n) 11.0581794764 493 404 491
Margin of Error Constant*Stdev of Estimate 25.015339859 474 382 481
CI Left Endpoint xbar-E 463.484660141 481 411 502
CI Right Endpoint xbar+E 513.515339859 499 407 511
499 430 524
Avg (xbar) 488.5 403.6 492.9
Stdev (sigma) 10.543560436 13.704824779 16.4008807352
Confidence Interval 463.484660141 ≤ x ≤ 513.515339859

CI for Diff of two Avg

CI for difference between two Averages
Sample #1 size n1 30
Sample #1 average x1bar 57.48
Sample #1 stdev s1 23.95
Sample #2 size n2 35
Sample #2 average x2bar 66.39
Sample #2 stdev s2 22.26
Sample standard deviation s 23.0533304759
Confidence Level c 0.95
Degree of Freedom df 63
Constant tc 1.9983405224
Stdev of Estimate sigma/sqrt(n) 5.735822521
Margin of Error Constant*Stdev of Estimate 11.4621265733
CI Left Endpoint x1bar-x2bar-E -20.3721265733
CI Right Endpoint x1bar-x2bar+E 2.5521265733
Confidence Interval -20.3721265733 ≤ μ1 -μ2 ≤ 2.5521265733

CI for Diff of two Prop.

CI for difference between two proportions
Treadmills Bikes
Sample #1 Size n1 708 n1=185 n2=123
Sample #1 successes x1 22 x1=67 x2=55
Proportion of sample #2 successes p1hat 0.0310734463
Sample #2 Size n2 156
Sample #2 successes x2 12
Proportion of sample #2 successes p2hat 0.0769230769
Confidence Level c 0.95
Constant zc 1.9599639845
Stdev of Estimate 0.0223089982
Margin of Error E 0.043724833
CI Left Endpoint p1hat-p2hat-E -0.0895744636
CI Right Endpoint p1hat-p2hat+E -0.0021247976
Confidence Interval -0.0895744636 ≤ π1 - π2 ≤ -0.0021247976

Critical Value zc

Critical Value Zc
c (Confidence Level) 0.95
Total tail area 0.05
Half tail area 0.025
norminv -1.9599639845
zc (Critical Value) 1.9599639845

Critical Value tc

Critical Value tc
n (Sample size) 16
c (Confidence Level) 0.95
Two tail area 0.05
Degree of freedom 15
tinv 2.1314495357
tc (Critical Value) 2.1314495357

Critical Values for Chi^2

Critical Values for Chi^2
Sample Size n 30
Degree of Freedom df 29
Confidence Level c 0.99
Two Tail area 0.01
Half Tail Area 0.005
Area to the right of ChiR^2 0.005
Area to the right of ChiL^2 0.995
Right Tail Critical Value ChiR^2 52.3356177983
Left Tail Critical Value ChiL^2 13.1211489527

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