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.