# Q1a) z-Test of a Single Population Mean

## SOLUTION

### Given

Sample mean:

Hypothesized population mean:

Population standard deviation:

Sample size:

### Hypotheses

#### Null Hypothesis

(The average customer watches 48 hours or less of a sport channel per month.)

#### Alternative Hypothesis

(The average customer watches more than 48 hours of a sport channel per month.)

### Test Statistic

We use the formula for the z-test of one population mean:

### Rejection Region

#### Critical Value

For a significance level , and since this is a right-tailed test (due to ), we find the critical z-value from the z-table as .

Reject the if

### Conclusion

Since the calculated z-value of is not greater than the critical z-value of , we do not reject the

Therefore, at the 1% significance level, we do not have sufficient evidence to conclude that the average customer watches more than 48 hours of a sport channel per month.

This means that the claim by the Advance cable network that the average customer watches 48 hours or less per month stands.