Question

Periodically, Merrill Lynch customers are asked to evaluate Merrill Lynch 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 α= .05 and test to see whether the consultant with more experience has the higher population mean service rating.

Consultant A: n = 16, x = 6.82, s = 0.64
Consultant B: n = 10, x = 6.25, s = 0.75

a. State the null and alternative hypotheses.
b. Compute the value of the test statistic.
c. What is the p-value?
d. What is your conclusion?

Answer 1

See the explanation

Explanation:

(a)

H0: Consultant with more experience has the higher population mean service rating.

H1: Consultant with more experience doesn't have the higher population mean service rating.

(b)

t = 1.9923 (see the attached image)

(c)

The degrees of freedom for the test statistic,

df = 16

The P-value of the one tailed t- test with 16 degrees of freedom is,

P−value = tdist(X,df,tails)

P-value = tdist(1.9923,16,1)

P-value = 0.032

(d)​

Since, P-value 0.032 is less than the significance level 0.05, there is an enough evidence to reject the null hypothesis.

Hence, there is a sufficient evidence to conclude that Consultant with more experience doesn't have the higher population mean service rating.

Hope this helps!