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# Null Hypotheses

Problem (Null Hypothesis)

A union of restaurant and foodservice workers would like to estimate this year's mean hourly wage, mu, of foodservice workers in the U.S. Last year's mean hourly wage was \$8.16, and there is reason to believe that this year's value is different from last year's.
The union decides to do a statistical test to see if the value has indeed changed. The union chooses a random sample of this year's wages, computes the mean of the sample to be \$7.79, and computes the standard deviation of the sample to be \$1.20.

Question

What are the null hypothesis (H0) and the alternative hypothesis (H1) that should be used for the test?
-H0: mu = (less than, greater than or equal to, greater than, less than or equal to, not equal to, equal to) (1.20, 7.79, 8.16)
-H1: mu= (less than, greater than or equal to, greater than, less than or equal to, not equal to, equal to) (1.20, 7.79, 8.16)
In the context of this test, what Type I error?
-A Type I error is (rejecting, failing to reject) the hypothesis that mu is (less than, greater than or equal to, greater than, less than or equal to, not equal to, equal to) (1.20, 7.79, 8.16) when, in fact, mu is (less than, greater than or equal to, greater than, less than or equal to, not equal to, equal to) (1.20, 7.79, 8.16).
-Suppose that the union decides not to reject the null hypothesis. What sort of error might it be making? (Type I, Type II)

#### Solution Preview

Problem (Null Hypothesis)

A union of restaurant and foodservice workers would like to estimate this year's mean hourly wage, mu, of foodservice workers in the U.S. Last year's mean hourly wage was \$8.16, and there is reason to believe that this year's value is different from last year's.
The union decides to do a statistical test to see if the value has indeed changed. The union chooses a random sample of this ...

#### Solution Summary

A union of restaurant and foodservice workers would like to estimate this year's mean hourly wage, mu, of foodservice workers in the U.S. Last year's mean hourly wage was \$8.16, and there is reason to believe that this year's value is different from last year's.

\$2.19