A union of restaurant and foodservice workers would like to estimate this year\'

Question

A union of restaurant and foodservice workers would like to estimate this year's mean hourly wage, of foodservice workers in the U.S. Last year's mean hourly wage was $8.14, and there is 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 $7.77, and computes the standard deviation of the sample to be $1.10. Based on this information, answer the questions below. What are the null hypothesis (H_0) and the alternative hypothesis (H_1) that should be used for the test? In the context of this test, what is a Type 1 error? Suppose that the union decides not to reject the null hypothesis. What sort of error might it be making?

Explanation / Answer

Here we have to test the hypothesis that,

H0 : mu = $8.14 Vs H1 : mu < $8.14

where mu is the population mean hourly wage.

Type I error = P(Reject H0 / H0 is true)

= P(mu < $8.14 / H0 : mu = $8.14)

A type I error is reject the null hypothesis that mu is less than $8.14 when infact mu is $8.14.

Suppose that the union decides not to reject the null hypothesis. Then this might be making type II error.

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