Periodically, Merrill Lynch customers are asked to evaluate Merrill Lynch financ

Question

Periodically, Merrill Lynch customers are asked to evaluate Merrill Lynch financial consultants and services (2000 Merrill Lynch Client Satisfaction Survey). 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 = .05 and test to see whether the consultant with more experience has the higher population mean service rating. Consultant A n_1 = 16 x_1 = 6.82 s_1 = .64 Consultant B n_2 = 10 x_2 = 6.25 s_2 = .75 a. State the null and alternative hypotheses. H_0: M_1 - M_2 H_a: mu_1 - mu_2 b. Compute the value of the test statistic (to 2 decimals). c. What is the p-value? d. What is your conclusion?

Explanation / Answer

b)

SE = sqrt[(s12/n1) + (s22/n2)]
SE = sqrt[(.64^2/16) + (.75^22/10]

= .2860

df = n1 + n2 - 2 = 16 + 10 -2 = 24

t = [ (x1 - x2) - d ] / SE

= [(6.82 - 6.25) - 0] / .2860

= 1.99

c) Now, we need to find p value by using t =1.99 and df = 24

p value = .0290

d) As , p value is less than alpha = 0.05 so, we reject the null hypothesis

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