Question

(5 points) According to the U.S. Census Bureau, 88% of Americans had at least a high school diploma or GED in 2015 and 33% had a bachelor's degree or more. 100 individuals with a high school diploma and no college were surveyed and their average annual salary was $34,436 with a standard deviation of $1643. 100 individuals with a bachelor's degree were also surveyed and their annual salary was $58,657 with a standard deviation of $2340. Carry out an appropriate hypothesis test to determine if individuals with a bachelor's degree have a higher annual salary, on average, than individuals with just a high school diploma. Make sure to include your hypotheses, assumptions and how they're satisfied, p-value, decision concerning the null hypothesis and an English statement explaining your findings.

Answer 1

Answenn Noro The null and Alternative hypothesis is: Hoiu, = 42 ولولا رلر ! والم This corresponds corresponds to a to a right-tailed test, for which a t-test for two population means, with two independent samples, with unknown population standard deviation will be wed. The significance level is d = 0.05 and df = 177.627 The critical value for this right -tailed test is for d=005 and df. 177.527. for this right tailed test is R = {tit) 1.6534. X-X Test statistic (t) te = 1.653 The rejection region 2 + ni where, xi=58657 7 q = 34436 3,- 2340 32 = 1643 > n = 100 and ną=100 Now, 58657-34436 to 23402 + 16432 100 100 .24221 54756 +26994,49

☺ at is observed that t = 84.712 >tc=1.653. 24221 381750.49 24221 285.9204 =84.7123 30, we reject the null hypothesis. Using the evalue approach. The pvalue is p= 0 and Since It is conclude that the null hypothesis is rejected P=O <0.05 Conclusions It is conclude that the null hypothesis to is rejected. .-. There is enough evidence to claim that population is greater than at the oon mean una Significance levet