Comparing Financial Consultant Ratings. 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.
- 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?
a.
State the null and alternative hypotheses.
Answer to Problem 17E
Null hypothesis:
Alternative hypothesis:
Explanation of Solution
Calculation:
The results from two independent samples of service ratings for financial consultant A and financial consultant B are as follows:
Consultant A | Consultant B |
Furthermore, it is given that consultant A has 10 years of experience and consultant B has 1 year experience and
State the hypotheses:
The test hypotheses are as follows:
Null hypothesis:
That is, the consultant with more experience has the lower population mean service rating.
Alternative hypothesis:
That is, the consultant with more experience has the higher population mean service rating.
b.
Find the value of test statistic.
Answer to Problem 17E
The value of the test statistic is 1.99.
Explanation of Solution
Calculation:
Test statistic:
The test statistic for hypothesis test of
Substitute
Thus, the test statistic is 1.99.
c.
Find the p-value.
Answer to Problem 17E
The p-value is 0.032.
Explanation of Solution
Degrees of freedom:
For t distribution with two independent random sample, the degrees of freedom is obtained as follows:
Substitute
Software procedure:
Step-by-step procedure to obtain the probability value using Excel:
- Open an EXCEL sheet and select the cell A1.
- Enter the formula =T.DIST.2T(1.99,15) in the cell A1.
- Press Enter.
Output using the EXCEL software is given below:
Thus, the p-value is 0.032.
d.
Obtain the conclusion whether the consultant with more experience has a higher population mean service rating or not.
Answer to Problem 17E
There is sufficient evidence to conclude that the consultant with more experience has the higher population mean service rating.
Explanation of Solution
Rejection rule:
If
If
Conclusion:
From part (c), the p-value is 0.032.
Here, the p-value is less than the level of significance.
That is,
From the rejection rule, the null hypothesis is rejected.
Therefore, the null hypothesis
Therefore, there is sufficient evidence to conclude that the consultant with more experience has the higher population mean service rating.
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Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill