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
Ho: µ = 18.4 -->population mean is equal to 18.4
Ha: µ < 18.4 -->population mean is less than 18.4
This would be a one-tailed test because the alternative hypothesis is showing a specific direction.
Note: The null hypothesis always uses an equals sign!
To formulate the null and alternative hypotheses for this study, we need to consider the information given.
The null hypothesis (H₀) states that there is no significant difference between the average amount of time spent watching television per week before and after the campaign. In this case, it would indicate that the average amount of time spent watching television per week remains the same or has not decreased.
The alternative hypothesis (H₁) states that there is a significant difference between the average amount of time spent watching television per week before and after the campaign. Specifically, it would indicate that the average amount of time spent watching television per week has decreased.
So, in symbol form:
Null hypothesis: H₀: μ = 18.4
Alternative hypothesis: H₁: μ < 18.4 (assuming the intention is to determine if it has decreased)