Periodically, customers of a financial services company are asked to evaluate the company's financial consultants and services. Higher ratings on the client
satisfaction survey indicate better service, with 7 the maximum service rating. Independent samples of service ratings for two financial consultants are
summarized here. Consultant A has 10 years of experience, whereas consultant B has 1 year of experience. Use $\alpha = 0.05$ and test to see whether the
consultant with more experience has the higher population mean service rating.
Consultant A Consultant B
$n_1 = 16$
$n_2 = 10$
$\bar{x}_1 = 6.82$
$\bar{x}_2 = 6.26$
$s_1 = 0.64$
$s_2 = 0.75$
(a) State the null and alternative hypotheses.
$H_0: \mu_1 - \mu_2 = 0$
$H_a: \mu_1 - \mu_2 > 0$
(b) Compute the value of the test statistic. (Round your answer to three decimal places.)
1.957
(c) What is the $p$-value? (Round your answer to four decimal places.)
p-value = 0.0257
(d) What is your conclusion?
Reject $H_0$. There is sufficient evidence to conclude that the consultant with more experience has a higher population mean rating.
