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. 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.

Excel File: data10-17.xls

a. State the null and alternative hypotheses.
H0 :
- Select your answer -
mu1 - mu2 is greater than 0
mu1 - mu2 is greater than or equal to 0
mu1 - mu2 is equal to 0
mu1 - mu2 is not equal to 0
mu1 - mu2 is less than 0
mu1 - mu2 is less than or equal to 0
Item 1

Ha :
- Select your answer -
mu1 - mu2 is greater than 0
mu1 - mu2 is greater than or equal to 0
mu1 - mu2 is equal to 0
mu1 - mu2 is not equal to 0
mu1 - mu2 is less than 0
mu1 - mu2 is less than or equal to 0
Item 2

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

c. What is the p-value? (to 4 decimals)
< p <

d. What is your conclusion?
- Select your answer -
Reject the null hypothesis
Do not reject the null hypothesis
Item 6

Explanation / Answer

Set Up Hypothesis
Null , There Is No-Significance between them Ho: u1 - u2 =0
Alternate,consultant with more experience has higher mean - H1: u1 - u2 >0
Test Statistic
X(Mean)=6.82
Standard Deviation(s.d1)=0.64 ; Number(n1)=16
Y(Mean)=6.25
Standard Deviation(s.d2)=0.75; 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((0.4096/16)+(0.5625/10))
to =1.992
| to | =1.992
Critical Value
The Value of |t | with Min (n1-1, n2-1) i.e 9 d.f is 1.833
We got |to| = 1.99235 & | t | = 1.833
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value:Right Tail -Ha : ( P > 1.9923 ) = 0.03875
Hence Value of P0.05 > 0.03875,Here we Reject Ho

[ANSWERS]
a. mu1 - mu2 is equal to 0
b. mu1 - mu2 is less than 0
c. to =1.99
d. p= 0.03875
e. Reject Ho

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