Periodically, customers of a financial services company are asked to evaluate the company's 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 a 0.05 and test to see whether the consultant with more experience has the higher population mean service rating. Consultant A Consultant B "116 2- 10 x- 6.05 X,- 6.25 $10.64 2- 0.75 (a) State the null and alternative hypotheses. O Hoi H- 2s 0 O Ho: H- H2 50 O Hoi H-H2>0 O Hoi H- H2*0 H H-2-0 O Ho! H- H2 - 0 (b) Compute the value of the test statistic. (Round your answer to three decimal places.) (c) What is the p-value? (Round your answer to four decimal places.) pvalue

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Topic Video
Question
Periodically, customers of a financial services company are asked to evaluate the company’s financial consultants and services. Higher ratings on the client satisfaction survey indicate better service, with 7 being 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 \(\alpha = 0.05\) and test to see whether the consultant with more experience has the higher population mean service rating.

### Data Summary
| Consultant A | Consultant B |
|--------------|--------------|
| \(n_1 = 16\) | \(n_2 = 10\) |
| \(\bar{x}_1 = 6.85\) | \(\bar{x}_2 = 6.25\) |
| \(s_1 = 0.64\) | \(s_2 = 0.75\) |

### Hypotheses
**(a) State the null and alternative hypotheses:**

- \(\text{H}_0\): \(\mu_1 - \mu_2 \leq 0\)  
  \(\text{H}_a\): \(\mu_1 - \mu_2 > 0\)

- \(\text{H}_0\): \(\mu_1 - \mu_2 \geq 0\)  
  \(\text{H}_a\): \(\mu_1 - \mu_2 < 0\)

- \(\text{H}_0\): \(\mu_1 - \mu_2 = 0\)  
  \(\text{H}_a\): \(\mu_1 - \mu_2 \neq 0\)

### Calculate and Conclude
**(b) Compute the value of the test statistic.**  
(Round your answer to three decimal places.)

**(c) What is the p-value?**  
(Round your answer to four decimal places.)  
p-value = \_\_\_\_

**(d) What is your conclusion?**

- Do not reject \(\text{H}_0\): There is insufficient evidence to conclude that the consultant with more experience has a higher population mean rating.

- Reject \(\text{H}_0\): There is sufficient evidence to conclude that the consultant with more experience has a higher population mean rating.
Transcribed Image Text:Periodically, customers of a financial services company are asked to evaluate the company’s financial consultants and services. Higher ratings on the client satisfaction survey indicate better service, with 7 being 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 \(\alpha = 0.05\) and test to see whether the consultant with more experience has the higher population mean service rating. ### Data Summary | Consultant A | Consultant B | |--------------|--------------| | \(n_1 = 16\) | \(n_2 = 10\) | | \(\bar{x}_1 = 6.85\) | \(\bar{x}_2 = 6.25\) | | \(s_1 = 0.64\) | \(s_2 = 0.75\) | ### Hypotheses **(a) State the null and alternative hypotheses:** - \(\text{H}_0\): \(\mu_1 - \mu_2 \leq 0\) \(\text{H}_a\): \(\mu_1 - \mu_2 > 0\) - \(\text{H}_0\): \(\mu_1 - \mu_2 \geq 0\) \(\text{H}_a\): \(\mu_1 - \mu_2 < 0\) - \(\text{H}_0\): \(\mu_1 - \mu_2 = 0\) \(\text{H}_a\): \(\mu_1 - \mu_2 \neq 0\) ### Calculate and Conclude **(b) Compute the value of the test statistic.** (Round your answer to three decimal places.) **(c) What is the p-value?** (Round your answer to four decimal places.) p-value = \_\_\_\_ **(d) What is your conclusion?** - Do not reject \(\text{H}_0\): There is insufficient evidence to conclude that the consultant with more experience has a higher population mean rating. - Reject \(\text{H}_0\): There is sufficient evidence to conclude that the consultant with more experience has a higher population mean rating.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Hypothesis Tests and Confidence Intervals for Means
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman