# Test

### Hypotheses

• Null Hypothesis : The average customer watches 48 hours or less of a sport channel per month. Mathematically, this is expressed as .
• Alternative Hypothesis : The average customer watches more than 48 hours of a sport channel per month. This is expressed as .

### Test Statistic

We use the formula for the z-test statistic for a sample mean:

where:

• is the sample mean, 49.6 hours.
• is the hypothesized population mean, 48 hours.
• is the population standard deviation, 9 hours.
• is the sample size, 48.

Calculating the z-value:

### Rejection Region

For a significance level of 1%, and since this is a right-tailed test (due to ), we find the critical z-value from z-tables or a standard normal distribution table.

The critical z-value for is approximately 2.33 (since we are looking at the area to the right of the curve).

### Conclusion

We compare the calculated z-value with the critical z-value:

• Calculated z-value: 1.23
• Critical z-value: 2.33

Since , we do not reject the null hypothesis.

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