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Over the years, the mean customer satisfaction rating at a local restaurant has been 79. The restaurant was recently remodeled, and now the management claims the mean customer rating, u, is not equal to 79. In a sample of 51 customers chosen at random, the mean customer rating is 79.3. Assume that the population standard deviation of customer ratings is 2.4. Is there enough evidence to support the claim that the mean customer rating is different from 79? Perform a hypothesis test, using the 0.10 level of significance. (a) State the null hypothesis H, and the alternative hypothesis H. Ho: D O

Over the years, the mean customer satisfaction rating at a local restaurant has been 79. The restaurant was recently remodeled, and now the management claims the mean customer rating, u, is not equal to 79. In a sample of 51 customers chosen at random, the mean customer rating is 79.3. Assume that the population standard deviation of customer ratings is 2.4. Is there enough evidence to support the claim that the mean customer rating is different from 79? Perform a hypothesis test, using the 0.10 level of significance. (a) State the null hypothesis H, and the alternative hypothesis H. Ho: D O

MATLAB: An Introduction with Applications
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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### Using the Standard Normal Distribution #### Steps to Conduct a Test: 1. **Select one-tailed or two-tailed:** - Options: - One-tailed - Two-tailed 2. **Enter the test statistic:** - Note: Round to 3 decimal places. 3. **Shade the area represented by the *p*-value:** - This step involves visualizing the area under the curve corresponding to the *p*-value. 4. **Enter the *p*-value:** - Note: Round to 3 decimal places. #### Graph Details: The graph shown is a standard normal distribution curve. It is symmetric and bell-shaped with the mean at the center (0) and standard deviations marked along the x-axis. The y-axis represents the probability density. #### Decision Making Based on Hypothesis Testing: **(c) Based on your answer to part (b), determine the conclusion at the 0.10 level of significance:** - **Options:** 1. Since the *p*-value is less than (or equal to) the level of significance, the null hypothesis is rejected. Thus, there is enough evidence to support the claim that the mean customer rating is not equal to 79. 2. Since the *p*-value is less than (or equal to) the level of significance, the null hypothesis is not rejected. Thus, there is not enough evidence to support the claim that the mean customer rating is not equal to 79. 3. Since the *p*-value is greater than the level of significance, the null hypothesis is rejected. Thus, there is enough evidence to support the claim that the mean customer rating is not equal to 79. 4. Since the *p*-value is greater than the level of significance, the null hypothesis is not rejected. Thus, there is not enough evidence to support the claim that the mean customer rating is not equal to 79. **Buttons:** - Explanation - Check © 2021 McGraw Hill LLC. All Rights Reserved.
Transcribed Image Text:### Using the Standard Normal Distribution #### Steps to Conduct a Test: 1. **Select one-tailed or two-tailed:** - Options: - One-tailed - Two-tailed 2. **Enter the test statistic:** - Note: Round to 3 decimal places. 3. **Shade the area represented by the *p*-value:** - This step involves visualizing the area under the curve corresponding to the *p*-value. 4. **Enter the *p*-value:** - Note: Round to 3 decimal places. #### Graph Details: The graph shown is a standard normal distribution curve. It is symmetric and bell-shaped with the mean at the center (0) and standard deviations marked along the x-axis. The y-axis represents the probability density. #### Decision Making Based on Hypothesis Testing: **(c) Based on your answer to part (b), determine the conclusion at the 0.10 level of significance:** - **Options:** 1. Since the *p*-value is less than (or equal to) the level of significance, the null hypothesis is rejected. Thus, there is enough evidence to support the claim that the mean customer rating is not equal to 79. 2. Since the *p*-value is less than (or equal to) the level of significance, the null hypothesis is not rejected. Thus, there is not enough evidence to support the claim that the mean customer rating is not equal to 79. 3. Since the *p*-value is greater than the level of significance, the null hypothesis is rejected. Thus, there is enough evidence to support the claim that the mean customer rating is not equal to 79. 4. Since the *p*-value is greater than the level of significance, the null hypothesis is not rejected. Thus, there is not enough evidence to support the claim that the mean customer rating is not equal to 79. **Buttons:** - Explanation - Check © 2021 McGraw Hill LLC. All Rights Reserved.
Over the years, the mean customer satisfaction rating at a local restaurant has been 79. The restaurant was recently remodeled, and now the management claims the mean customer rating, μ, is not equal to 79. In a sample of 51 customers chosen at random, the mean customer rating is 79.3. Assume that the population standard deviation of customer ratings is 2.4. Is there enough evidence to support the claim that the mean customer rating is different from 79? Perform a hypothesis test, using the 0.10 level of significance. (a) State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \): - \( H_0 : \mu = 79 \) - \( H_1 : \mu \neq 79 \) (b) Perform a Z-test and find the p-value. Here is some information to help you with your Z-test: - The value of the test statistic is given by \( \frac{\bar{x} - \mu}{\sigma/\sqrt{n}} \) - The p-value is two times the area under the curve to the right of the value of the test statistic. **Graph Description:** The graph displays a standard normal distribution curve. A vertical line represents the Z-test statistic's value, which separates the curve into two tails. The shaded area to the right indicates the p-value for a two-tailed test. **Steps:** 1. **Select one-tailed or two-tailed:** - One-tailed - Two-tailed (selected for this test) 2. **Enter the test statistic:** (Round to 3 decimal places) **Note:** The test involves assessing whether the customer's mean satisfaction rating has significantly changed from the historical mean of 79, considering an alpha level of 0.10 for the hypothesis test.
Transcribed Image Text:Over the years, the mean customer satisfaction rating at a local restaurant has been 79. The restaurant was recently remodeled, and now the management claims the mean customer rating, μ, is not equal to 79. In a sample of 51 customers chosen at random, the mean customer rating is 79.3. Assume that the population standard deviation of customer ratings is 2.4. Is there enough evidence to support the claim that the mean customer rating is different from 79? Perform a hypothesis test, using the 0.10 level of significance. (a) State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \): - \( H_0 : \mu = 79 \) - \( H_1 : \mu \neq 79 \) (b) Perform a Z-test and find the p-value. Here is some information to help you with your Z-test: - The value of the test statistic is given by \( \frac{\bar{x} - \mu}{\sigma/\sqrt{n}} \) - The p-value is two times the area under the curve to the right of the value of the test statistic. **Graph Description:** The graph displays a standard normal distribution curve. A vertical line represents the Z-test statistic's value, which separates the curve into two tails. The shaded area to the right indicates the p-value for a two-tailed test. **Steps:** 1. **Select one-tailed or two-tailed:** - One-tailed - Two-tailed (selected for this test) 2. **Enter the test statistic:** (Round to 3 decimal places) **Note:** The test involves assessing whether the customer's mean satisfaction rating has significantly changed from the historical mean of 79, considering an alpha level of 0.10 for the hypothesis test.
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