Periodically, Merrill Lynch customers are asked to evaluate Merrill Lynch financial consultants and services on a 7-point scale (7 is the maximum). You ar a manager with two consultants you are trying to compare. Consultant A has 10 years of experience, whereas consultant B has 1 year of experience. You want to test the claim that the consultant with more experience has the higher mear service rating. So, you collect independent samples of service ratings for these two financial consultants. Consultant A has 25 surveys with a mean of 6.48 and standard deviation of 0.4: Consultant B has 28 surveys with a mean of 6.31 and standard deviation of 0.42 You wish to test the claim at a significance level of a=0.10 Ho: H1 – µ2 = 0 Ha: H1 – H2 > 0 (In this setup, Consultant A is sample 1 and Consultant B is sample 2) a) Find the test statistic. b) Find the p-value c) State the conclusion (in the context of the problem).
Periodically, Merrill Lynch customers are asked to evaluate Merrill Lynch financial consultants and services on a 7-point scale (7 is the maximum). You ar a manager with two consultants you are trying to compare. Consultant A has 10 years of experience, whereas consultant B has 1 year of experience. You want to test the claim that the consultant with more experience has the higher mear service rating. So, you collect independent samples of service ratings for these two financial consultants. Consultant A has 25 surveys with a mean of 6.48 and standard deviation of 0.4: Consultant B has 28 surveys with a mean of 6.31 and standard deviation of 0.42 You wish to test the claim at a significance level of a=0.10 Ho: H1 – µ2 = 0 Ha: H1 – H2 > 0 (In this setup, Consultant A is sample 1 and Consultant B is sample 2) a) Find the test statistic. b) Find the p-value c) State the conclusion (in the context of the problem).
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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![Periodically, Merrill Lynch customers are asked to evaluate Merrill Lynch financial consultants and services on a 7-point scale (7 is the maximum). You are a manager with two consultants you are trying to compare. Consultant A has 10 years of experience, whereas Consultant B has 1 year of experience. You want to test the claim that the consultant with more experience has the higher mean service rating. So, you collect independent samples of service ratings for these two financial consultants.
Consultant A has 25 surveys with a mean of 6.48 and standard deviation of 0.41.
Consultant B has 28 surveys with a mean of 6.31 and standard deviation of 0.42.
You wish to test the claim at a significance level of α=0.10.
\[ H_0: \mu_1 - \mu_2 = 0 \]
\[ H_a: \mu_1 - \mu_2 > 0 \]
(In this setup, Consultant A is sample 1 and Consultant B is sample 2)
a) Find the test statistic.
b) Find the p-value.
c) State the conclusion (in the context of the problem).
---
**Solution Outline:**
a) To find the test statistic:
We use the formula for the test statistic for the difference of means with independent samples:
\[ t = \frac{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)}{s_p \sqrt{\frac{1}{n_1} + \frac{1}{n_2}}} \]
Where:
\[ s_p = \sqrt{\frac{(n_1 - 1)s_1^2 + (n_2 - 1)s_2^2}{n_1 + n_2 - 2}} \]
Given:
\[ \bar{x}_1 = 6.48, \quad s_1 = 0.41, \quad n_1 = 25 \]
\[ \bar{x}_2 = 6.31, \quad s_2 = 0.42, \quad n_2 = 28 \]
First, calculate the pooled standard deviation \( s_p \):
\[ s_p = \sqrt{\frac{(25 - 1) \times 0.41^2 + (28 - 1) \times 0.42^2}{25 +](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F167c4a57-20fc-4ce6-9a90-f7ea4d81de63%2F3c9803ca-7472-4220-83c0-ec2c65e4206c%2F1scz2qs_processed.png&w=3840&q=75)
Transcribed Image Text:Periodically, Merrill Lynch customers are asked to evaluate Merrill Lynch financial consultants and services on a 7-point scale (7 is the maximum). You are a manager with two consultants you are trying to compare. Consultant A has 10 years of experience, whereas Consultant B has 1 year of experience. You want to test the claim that the consultant with more experience has the higher mean service rating. So, you collect independent samples of service ratings for these two financial consultants.
Consultant A has 25 surveys with a mean of 6.48 and standard deviation of 0.41.
Consultant B has 28 surveys with a mean of 6.31 and standard deviation of 0.42.
You wish to test the claim at a significance level of α=0.10.
\[ H_0: \mu_1 - \mu_2 = 0 \]
\[ H_a: \mu_1 - \mu_2 > 0 \]
(In this setup, Consultant A is sample 1 and Consultant B is sample 2)
a) Find the test statistic.
b) Find the p-value.
c) State the conclusion (in the context of the problem).
---
**Solution Outline:**
a) To find the test statistic:
We use the formula for the test statistic for the difference of means with independent samples:
\[ t = \frac{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)}{s_p \sqrt{\frac{1}{n_1} + \frac{1}{n_2}}} \]
Where:
\[ s_p = \sqrt{\frac{(n_1 - 1)s_1^2 + (n_2 - 1)s_2^2}{n_1 + n_2 - 2}} \]
Given:
\[ \bar{x}_1 = 6.48, \quad s_1 = 0.41, \quad n_1 = 25 \]
\[ \bar{x}_2 = 6.31, \quad s_2 = 0.42, \quad n_2 = 28 \]
First, calculate the pooled standard deviation \( s_p \):
\[ s_p = \sqrt{\frac{(25 - 1) \times 0.41^2 + (28 - 1) \times 0.42^2}{25 +
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