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Two-Sample Hypothesis Tests

This document provides solutions for two-sample hypothesis testing problems.

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Due by 11.59pmJuly 20th1Chapter 10Two-Sample Hypothesis TestsAssignmentPlease providedetailed solutions to the following problems/exercises (4problems/exercises x8pointseach):1) Discover Card would like to test the hypothesis that the average credit score for an adult in Dallas isdifferent from the average credit score for an adult in Houston. A random sample of 40 adults in Dallashad an average credit score of 699 and a random sample of 35 adults in Houston had an average creditscore of 682. It is believed that the population standard deviation for credit scores is 44 and 41 for Dallasand Houston residents, respectively. Discover Card would like to setฮฑ= 0.05. Define Population 1 asDallas and Population 2 as Houston and use the critical value approach to test this hypothesis.Null Hypothesis:๐ป0:ฮผ1โˆ’ฮผ2=0Alternative Hypothesis:๐ปเฏ”:ฮผ1โˆ’ฮผ2โ‰ 0Type of test:Z test for two population mean(two tailed) assumingequal variance.Test Statistic:Pooled variance(๐‘†2)=(๐‘›1โˆ’1)โˆ—๐‘†12+(๐‘›2โˆ’1)โˆ—๐‘†22๐‘›1+๐‘›2โˆ’2=39โˆ—442+34โˆ—41240+35โˆ’2=1817.232877Test Statistic =๐‘‹เดค1โˆ’๐‘‹เดค2เถง๐‘†2โˆ—แ‰€1๐‘›1+1๐‘›2แ‰=699โˆ’682เถง1817.232877โˆ—แ‰€140+135แ‰=1.7230Rejection region:As this is a two tailed test so thecritical value is Z(0.025) = 1.96The rejection region is,|Test Statistic| > Critical value = 1.96Conclusion:The test statistic is not falling in the rejection region thus we arefailing torejectthe null hypothesis.Conclusion isthere is not a significant difference between theaverage credit score for an adult in DallasandHouston.2) Auto Trader Group (ATG) would like to test the hypothesis that the average age of an imported car onthe road is greater than the average age of a domestic car. The following data shows the sample size andthe average age of cars for import and domestic cars along with the population standard deviations.DomesticImport

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