Periodically Merrill Lynch customers are asked to evaluate M

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.

s.
H₀: ₁ - ₂
H_a: ₁ - ₂

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

What is the p-value?
The p-value is

What is your conclusion?

Solution

Set Up Hypothesis
Null, Ho: u1 = u2
Alternate, consultant with more experience has the higher population mean - H1: u1 > u2
Test Statistic
X(Mean)=6.82
Standard Deviation(s.d1)=0.7 ; Number(n1)=16
Y(Mean)=6.25
Standard Deviation(s.d2)=0.8; Number(n2)=10
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =6.82-6.25/Sqrt((0.49/16)+(0.64/10))
to =1.853
| to | =1.853
Critical Value
The Value of |t | with Min (n1-1, n2-1) i.e 9 d.f is 1.833
We got |to| = 1.85299 & | t | = 1.833
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value:Right Tail -Ha : ( P > 1.853 ) = 0.04844
Hence Value of P0.05 > 0.04844,Here we Reject Ho

We have evidence to indicate consultant with more experience has the higher population mean