A union of restaurant and foodservice workers would like to estimate the mean hourly wage, µ, 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 $7.68, and computes the standard deviation of the sample to be $1.20. Based on this information, complete the parts below. (a) what are the null hypothesis H, and the alternative hypothesis H, that should be used for the test? H, : O
A union of restaurant and foodservice workers would like to estimate the mean hourly wage, µ, 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 $7.68, and computes the standard deviation of the sample to be $1.20. Based on this information, complete the parts below. (a) what are the null hypothesis H, and the alternative hypothesis H, that should be used for the test? H, : O
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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Transcribed Image Text:**Statistical Hypothesis Testing for Mean Hourly Wage**
A union of restaurant and foodservice workers is interested in determining whether the mean hourly wage, \( \mu \), for workers in the U.S. this year has decreased compared to last year. The mean hourly wage last year was $8.08, and there is reason to believe that the current year's wage is lower.
The union conducts a statistical test by drawing a random sample and finds the mean of this sample to be $7.68, with a computed standard deviation of $1.20.
**Null and Alternative Hypotheses**
(a) **Formulate Hypotheses:**
- **Null Hypothesis (\( H_0 \))**: \( \mu = 8.08 \)
- **Alternative Hypothesis (\( H_1 \))**: \( \mu < 8.08 \)
(b) **Deciding on the Correct Error Type**
Suppose the union decides not to reject the null hypothesis. Consider the possible error:
- The potential error in not rejecting the null hypothesis when it is false is a **Type II error**.
(c) **Understanding Type I Error**
Suppose that the actual mean wage is indeed $8.08. Describe a Type I error:
- A **Type I error** occurs when we reject the hypothesis that \( \mu = 8.08 \) (choosing \( \mu < 8.08 \)) when, in fact, \( \mu \) is actually equal to 8.08.
**Tip:** It is crucial to correctly understand and interpret both Type I and Type II errors to validate the results of statistical tests in hypothesis testing.
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