Two-Sample Hypothesis Tests
This document provides solutions for two-sample hypothesis testing problems.
Andrew Taylor
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1
Chapter 10
Two-Sample Hypothesis Tests
Assignment
Please provide detailed solutions to the following problems/exercises (4 problems/exercises x 8 points
each):
1) Discover Card would like to test the hypothesis that the average credit score for an adult in Dallas is
different from the average credit score for an adult in Houston. A random sample of 40 adults in Dallas
had an average credit score of 699 and a random sample of 35 adults in Houston had an average credit
score of 682. It is believed that the population standard deviation for credit scores is 44 and 41 for Dallas
and Houston residents, respectively. Discover Card would like to set ฮฑ = 0.05. Define Population 1 as
Dallas and Population 2 as Houston and use the critical value approach to test this hypothesis.
Null Hypothesis:
๐ป0: ฮผ1 โ ฮผ2 = 0
Alternative Hypothesis:
๐ปเฏ: ฮผ1 โ ฮผ2 โ 0
Type of test:
Z test for two population mean(two tailed) assuming equal variance.
Test Statistic:
Pooled variance (๐2) = (๐1โ1)โ๐1
2+(๐2โ1)โ๐2
2
๐1+๐2โ2 = 39โ442+34โ412
40+35โ2 = 1817.232877
Test Statistic = ๐เดค1โ๐เดค2
เถง๐2โแ 1
๐1+ 1
๐2แ
= 699โ682
เถง1817.232877โแ 1
40+ 1
35แ
= 1.7230
Rejection region:
As this is a two tailed test so the critical value is Z(0.025) = 1.96
The rejection region is,
|Test Statistic| > Critical value = 1.96
Conclusion:
The test statistic is not falling in the rejection region thus we are failing to reject the null hypothesis.
Conclusion is there is not a significant difference between the average credit score for an adult in Dallas
and Houston.
2) Auto Trader Group (ATG) would like to test the hypothesis that the average age of an imported car on
the road is greater than the average age of a domestic car. The following data shows the sample size and
the average age of cars for import and domestic cars along with the population standard deviations.
Domestic Import
1
Chapter 10
Two-Sample Hypothesis Tests
Assignment
Please provide detailed solutions to the following problems/exercises (4 problems/exercises x 8 points
each):
1) Discover Card would like to test the hypothesis that the average credit score for an adult in Dallas is
different from the average credit score for an adult in Houston. A random sample of 40 adults in Dallas
had an average credit score of 699 and a random sample of 35 adults in Houston had an average credit
score of 682. It is believed that the population standard deviation for credit scores is 44 and 41 for Dallas
and Houston residents, respectively. Discover Card would like to set ฮฑ = 0.05. Define Population 1 as
Dallas and Population 2 as Houston and use the critical value approach to test this hypothesis.
Null Hypothesis:
๐ป0: ฮผ1 โ ฮผ2 = 0
Alternative Hypothesis:
๐ปเฏ: ฮผ1 โ ฮผ2 โ 0
Type of test:
Z test for two population mean(two tailed) assuming equal variance.
Test Statistic:
Pooled variance (๐2) = (๐1โ1)โ๐1
2+(๐2โ1)โ๐2
2
๐1+๐2โ2 = 39โ442+34โ412
40+35โ2 = 1817.232877
Test Statistic = ๐เดค1โ๐เดค2
เถง๐2โแ 1
๐1+ 1
๐2แ
= 699โ682
เถง1817.232877โแ 1
40+ 1
35แ
= 1.7230
Rejection region:
As this is a two tailed test so the critical value is Z(0.025) = 1.96
The rejection region is,
|Test Statistic| > Critical value = 1.96
Conclusion:
The test statistic is not falling in the rejection region thus we are failing to reject the null hypothesis.
Conclusion is there is not a significant difference between the average credit score for an adult in Dallas
and Houston.
2) Auto Trader Group (ATG) would like to test the hypothesis that the average age of an imported car on
the road is greater than the average age of a domestic car. The following data shows the sample size and
the average age of cars for import and domestic cars along with the population standard deviations.
Domestic Import
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