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?

See the explanation

Step-by-step 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!

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