Question

A union of restaurant and foodservice workers would like to estimate this year's mean hourly wage, u, of foodservice workers in the U.S. Last year's mean hourly wage was $8.08, and there is reason to believe that this year's value is greater than last year's. The union decides to do a statistical test to see if the value has indeed increased. The union chooses a random sample of this year's wages, computes the mean of the sample to be $8.45, and computes the standard deviation of the sample to be $1.25. Based on this information, answer the questions below. What are the null hypothesis (1) and the alternative hypothesis (H) that should be used for the test? ? Ho: His? H: his . ? In the context of this test, what is a Type I error? A Type I error is? when, in fact, u is? the hypothesis that u is? ? ? Suppose that the union decides not to reject the null hypothesis. What sort of error might it be making? 2 х 5 ?

Answer 1

Solution:

1)

H₀ : $\mu$ is = (equal to) 8.08

H₀ : $\mu$ is > (greater than) 8.08

2)

A Type I error is rejecting the hypothesis that $\mu$ is = (equal to) 8.08 , when , in fact , $\mu$ is = (equal to) 8.08.

(because Type I error is Reject the null hypothesis when the null hypothesis is true)

3)

Type II error