A union of restaurant and foodservice workers would like to estimate the mean hourly wage, u, of foodservice workers in the U.S. this year The mean hourly wage last year was $8.08, and there is good reason to believe that this year's value is less than last year's. The union decides to do a statistical test to see if the value has indeed decreased. The union chooses a random sample of this year's wages, computes the mean of the sample to be $7.78, and computes the standard deviation of the sample to be $1.10. Based on this information, complete the parts below.
A union of restaurant and foodservice workers would like to estimate the mean hourly wage, u, of foodservice workers in the U.S. this year The mean hourly wage last year was $8.08, and there is good reason to believe that this year's value is less than last year's. The union decides to do a statistical test to see if the value has indeed decreased. The union chooses a random sample of this year's wages, computes the mean of the sample to be $7.78, and computes the standard deviation of the sample to be $1.10. Based on this information, complete the parts below.
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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![**Educational Website Transcription**
A union of restaurant and food service workers aims to estimate the mean hourly wage, \( \mu \), of food service workers in the U.S. for this year. Last year's mean hourly wage was $8.08, and there is evidence to believe that this year's value is less than last year's.
The union decides to perform a statistical test to determine if the mean wage has decreased. They choose a random sample of this year's wages and calculate the mean of the sample as $7.78, with a standard deviation of $1.10.
Based on this information, complete the following:
(a) **Hypothesis Testing**
- What are the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \) for the test?
\[
H_0 : [\text{Null hypothesis input}]
\]
\[
H_1 : [\text{Alternative hypothesis input}]
\]
(b) **Decision Making**
- Suppose that the union decides not to reject the null hypothesis. What sort of error might it be making?
\[
[\text{Choose one option from Type I or Type II error}]
\]
(c) **Understanding Type I Error**
- Suppose the true mean hourly wage for food service workers in the U.S. this year is $8.08. Fill in the blanks to describe a Type I error.
A Type I error would be [Choose one: rejecting/not rejecting] the hypothesis that \( \mu \) is [Choose one: greater than/less than/equal to] $8.08 when, in fact, \( \mu \) is [Choose one: greater than/less than/equal to] $8.08.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Febf69441-5213-4ecd-ae7f-e18417ae6fdf%2F5fca85d4-00af-40a3-8a3b-16f5f624e57d%2Fyd75g29_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Website Transcription**
A union of restaurant and food service workers aims to estimate the mean hourly wage, \( \mu \), of food service workers in the U.S. for this year. Last year's mean hourly wage was $8.08, and there is evidence to believe that this year's value is less than last year's.
The union decides to perform a statistical test to determine if the mean wage has decreased. They choose a random sample of this year's wages and calculate the mean of the sample as $7.78, with a standard deviation of $1.10.
Based on this information, complete the following:
(a) **Hypothesis Testing**
- What are the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \) for the test?
\[
H_0 : [\text{Null hypothesis input}]
\]
\[
H_1 : [\text{Alternative hypothesis input}]
\]
(b) **Decision Making**
- Suppose that the union decides not to reject the null hypothesis. What sort of error might it be making?
\[
[\text{Choose one option from Type I or Type II error}]
\]
(c) **Understanding Type I Error**
- Suppose the true mean hourly wage for food service workers in the U.S. this year is $8.08. Fill in the blanks to describe a Type I error.
A Type I error would be [Choose one: rejecting/not rejecting] the hypothesis that \( \mu \) is [Choose one: greater than/less than/equal to] $8.08 when, in fact, \( \mu \) is [Choose one: greater than/less than/equal to] $8.08.
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