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 = .05 and test to see whether the consultant with more experience has the higher population mean service rating.

Compute the value of the test statistic (to 2 decimals).
____________

What is the p-value? Use z-table.
The p-value is ________

What is your conclusion?

State the null and alternative hypotheses.
H0: 1 - 2 ___________
Ha: 1 - 2 ___________

Compute the value of the test statistic (to 2 decimals).
____________

What is the p-value? Use z-table.
The p-value is ________

What is your conclusion?

Consultant A Consultant B n1 X 1 = 6.82 S 1 = 0.58 10 X 2 = 6.25 s2=0.7

Explanation / Answer

as we need to check

whether the consultant with more experience has the higher population mean service rating.

Hence the difference must be greater than 0

so

H0 : difference is less than or equal to 0
H1 : difference is greater than 0

we calculate the z stat

as

Z = (x1bar-x2bar)/sqrt(s1^2/n1 + s2^2/n2)

= (6.82-6.25)/sqrt(0.58^2/16 + 0.7^2/10)

= 2.154

now we check the z table to find p(z>2.154) from the z table
P ( Z>2.154 )=1P ( Z<2.154 )=10.9842=0.0158

as the p value is less than 0.05 , hence we reject null hypothesis in favor of alternate hypothesis and conclude that
difference is greater than 0

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