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 23 surveys with a mean of 6.46 and standard deviation of 0.66. Consultant B has 27 surveys with a mean of 6.37 and standard deviation of 0.43. You wish to test the claim at a significance level of a = 0.005. a. What is the test statistic for this sample? test statistic = Round to 4 decimal places. b. What is the p-value for this sample? p-value = Round to 4 decimal places. c. The p-value is... less than (or equal to) a O greater than a d. This test statistic leads to a decision to... O reject the null O accept the null O fail to reject the null e. As such, the final conclusion is that...

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 23 surveys with a mean of 6.46 and standard deviation of 0.66. Consultant B has 27 surveys with a mean of 6.37 and standard deviation of 0.43. You wish to test the claim at a significance level of a = 0.005. a. What is the test statistic for this sample? test statistic = Round to 4 decimal places. b. What is the p-value for this sample? p-value = Round to 4 decimal places. c. The p-value is... less than (or equal to) a O greater than a d. This test statistic leads to a decision to... O reject the null O accept the null O fail to reject the null e. As such, the final conclusion is that...

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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help

### Merrill Lynch Financial Consultants Service Evaluation

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.

To perform this analysis, you collect independent samples of service ratings for these two financial consultants. Consultant A has 23 surveys with a mean of 6.46 and a standard deviation of 0.66. Consultant B has 27 surveys with a mean of 6.37 and a standard deviation of 0.43. You wish to test this claim at a significance level of $\alpha = 0.005$.

#### Problem Statement:
1. **What is the test statistic for this sample?**
- **test statistic =** _______ (Round to 4 decimal places)

2. **What is the p-value for this sample?**
- **p-value =** _______ (Round to 4 decimal places)

3. **The p-value is...**
- $\circ$ less than (or equal to) $\alpha$
- $\circ$ greater than $\alpha$

4. **This test statistic leads to a decision to...**
- $\circ$ reject the null
- $\circ$ accept the null
- $\circ$ fail to reject the null

5. **As such, the final conclusion is that...**

#### Analysis Explanation:
To compare the means of the two samples provided, a two-sample t-test can be conducted. The test involves:
- Calculating the test statistic using the sample means, standard deviations, and sizes.
- Determining the p-value to understand the probability of observing the test results under the null hypothesis.
- Comparing the p-value with the significance level $\alpha$ to make a decision regarding the null hypothesis.

This analysis will help determine if the difference in service ratings between the two consultants is statistically significant.

**Note:** If you have any questions or need assistance with the calculations, please refer to your textbook or consult your instructor.

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