Due by 11 .59 pm July 2 0th 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 α = 0.05. Define Population 1 as Dallas and Population 2 as Houston and use the critical value approach to test this hypothesis. Null Hypothesis: 𝐻 0 : μ 1 − μ 2 = 0 Alternative Hypothesis: 𝐻 ௔ : μ 1 − μ 2 ≠ 0 Type of test: Z test for two population mean(two tailed) assuming equal variance. Test Statistic : Pooled variance ( 𝑆 2 ) = ( 𝑛 1 − 1 ) ∗ 𝑆 1 2 + ( 𝑛 2 − 1 ) ∗ 𝑆 2 2 𝑛 1 + 𝑛 2 − 2 = 39 ∗ 44 2 + 34 ∗ 41 2 40 + 35 − 2 = 1817.232877 Test Statistic = 𝑋 ത 1 − 𝑋 ത 2 ට 𝑆 2 ∗ ቀ 1 𝑛 1 + 1 𝑛 2 ቁ = 699 − 682 ට 1817 . 232877 ∗ ቀ 1 40 + 1 35 ቁ = 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: T he 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