(a) State the nul hypothesis H, and the alternative hypothesis H. 5 ? test"). Here is some ather information to help you with your (b) Perform a hypothesis test. The test statistic has a normal distribution (so the test test. as is the value that cuts off an area of 0.05 in the right tail. • The test statistic has a normal distribution and the value is given by = Standard Normal Distribution Stup 1: Salea onetaled or tao aled. O One-taled O Teed Stup 2 Enter the cical vala (ound to decimal placs) Stup Enter the test at (und to 3 decmal places) (c) Based on your answer to part (b), choose what can be concluded, at the 0.10 level of significance, about the claim made by the management.
(a) State the nul hypothesis H, and the alternative hypothesis H. 5 ? test"). Here is some ather information to help you with your (b) Perform a hypothesis test. The test statistic has a normal distribution (so the test test. as is the value that cuts off an area of 0.05 in the right tail. • The test statistic has a normal distribution and the value is given by = Standard Normal Distribution Stup 1: Salea onetaled or tao aled. O One-taled O Teed Stup 2 Enter the cical vala (ound to decimal placs) Stup Enter the test at (und to 3 decmal places) (c) Based on your answer to part (b), choose what can be concluded, at the 0.10 level of significance, about the claim made by the management.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![**Educational Website Explanation:**
---
**Hypothesis Testing Overview:**
The scenario explores whether sufficient evidence exists to claim that the mean customer satisfaction rating at a local restaurant, previously 79, has changed following a renovation. The management theorizes that the new mean rating, \(\mu\), is no longer 79. A sample of 31 customers gives an average rating of 78.3, with a known population standard deviation of 7.6. Using a significance level of 0.10, a hypothesis test is conducted.
**(a) Defining Hypotheses:**
- **Null Hypothesis (\(H_0\)):** \(\mu = 79\)
- **Alternative Hypothesis (\(H_1\)):** \(\mu \neq 79\)
**(b) Performing the Hypothesis Test:**
- **Test Statistic:** In this context, a z-test is used because the sample size is large and the population standard deviation is known. The test statistic (\(z\)) is calculated using:
\[
z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}
\]
Where:
\(\bar{x} = 78.3\) (sample mean),
\(\mu = 79\) (hypothesized mean),
\(\sigma = 7.6\) (population standard deviation),
\(n = 31\) (sample size).
- **Critical Value:** \(z_{0.05}\) is the critical z-value for a two-tailed test at a significance level of 0.10, split to 0.05 in each tail.
**Standard Normal Distribution:**
The diagram illustrates the standard normal distribution, highlighting critical areas for hypothesis testing:
1. **Select Test Type:** Two-tailed is selected.
2. **Critical Values:** The critical values that form the rejection regions are entered.
3. **Enter Test Statistic:** The calculated test statistic is inserted to determine its location relative to the critical regions.
**(c) Conclusion at 0.10 Significance Level:**
The outcome is determined based on where the test statistic falls:
- If the test statistic lands in the rejection region, it provides enough evidence to reject \(H_0\), supporting the claim that the mean customer rating is not 79.
- If the test statistic is not in the rejection region, there's insufficient](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbce1f951-db00-41fc-b226-5b8bf4ea58a6%2Ffff5df05-922b-4d3d-9819-3dca52a82954%2F5wk5l4o_processed.png&w=3840&q=75)
Transcribed Image Text:**Educational Website Explanation:**
---
**Hypothesis Testing Overview:**
The scenario explores whether sufficient evidence exists to claim that the mean customer satisfaction rating at a local restaurant, previously 79, has changed following a renovation. The management theorizes that the new mean rating, \(\mu\), is no longer 79. A sample of 31 customers gives an average rating of 78.3, with a known population standard deviation of 7.6. Using a significance level of 0.10, a hypothesis test is conducted.
**(a) Defining Hypotheses:**
- **Null Hypothesis (\(H_0\)):** \(\mu = 79\)
- **Alternative Hypothesis (\(H_1\)):** \(\mu \neq 79\)
**(b) Performing the Hypothesis Test:**
- **Test Statistic:** In this context, a z-test is used because the sample size is large and the population standard deviation is known. The test statistic (\(z\)) is calculated using:
\[
z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}
\]
Where:
\(\bar{x} = 78.3\) (sample mean),
\(\mu = 79\) (hypothesized mean),
\(\sigma = 7.6\) (population standard deviation),
\(n = 31\) (sample size).
- **Critical Value:** \(z_{0.05}\) is the critical z-value for a two-tailed test at a significance level of 0.10, split to 0.05 in each tail.
**Standard Normal Distribution:**
The diagram illustrates the standard normal distribution, highlighting critical areas for hypothesis testing:
1. **Select Test Type:** Two-tailed is selected.
2. **Critical Values:** The critical values that form the rejection regions are entered.
3. **Enter Test Statistic:** The calculated test statistic is inserted to determine its location relative to the critical regions.
**(c) Conclusion at 0.10 Significance Level:**
The outcome is determined based on where the test statistic falls:
- If the test statistic lands in the rejection region, it provides enough evidence to reject \(H_0\), supporting the claim that the mean customer rating is not 79.
- If the test statistic is not in the rejection region, there's insufficient
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
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
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
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
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
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
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman