At one school, the average amount of time that tenth-graders spend watching television each week is 18.4 hours. The principal introduces a campaign to encourage the students to watch less television. One year later, the principal wants to perform a hypothesis test to determine whether the average amount of time spent watching television per week has decreased. Formulate the null and alternative hypotheses for the study described.

Null:

Ho: µ = 18.4 -->population mean is equal to 18.4

Alternative:

Ha: µ < 18.4 -->population mean is less than 18.4

At one high school, the average amount of time tenth-graders spend watching television each week is The principal introduces a campaign to encourage the students to watch less television. One year later, the principal wants to perform a hypothesis test to determine whether the average amount of time spent watching television per week has decreased.

The null hypothesis (H0) for this study would be that there is no significant decrease in the average amount of time spent watching television per week by tenth-graders after the campaign.

The alternative hypothesis (H1) would be that there is a significant decrease in the average amount of time spent watching television per week by tenth-graders after the campaign.

To formulate the null and alternative hypotheses for this study, we need to define our variables and determine the direction of the hypothesis test.

Let's denote the average amount of time spent watching television per week by tenth-graders before the campaign as μ0 (population mean) and after the campaign as μ (sample mean).

Null hypothesis (H0): The average amount of time spent watching television per week has not changed after the campaign, i.e., μ = μ0. This implies that the mean time spent watching TV per week is still 18.4 hours.

Alternative hypothesis (Ha): The average amount of time spent watching television per week has decreased after the campaign, i.e., μ < μ0. This implies that the mean time spent watching TV per week is now less than 18.4 hours.

In summary:
Null hypothesis (H0): μ = μ0
Alternative hypothesis (Ha): μ < μ0

The null hypothesis assumes that there is no change in the average time spent watching television per week, while the alternative hypothesis suggests that there has been a decrease in the average time spent watching TV per week.