Question

education researchers conducted a study in order to estimate μ, the mean number of hours that high school students spent per week doing homework. suppose a random sample of 121 high school students shows a mean weekly homework time of 6.8 hours and that from prior studies, the population standard deviation is assumed to be σ = 2.8 hours. a similar study conducted a year earlier estimated that μ, the mean number of hours that high school students spent per week doing homework, was 6 hours. we would like to test (at the usual significance level of 5%) whether the current study provides significant evidence that this mean has changed since the previous year. using a 95% confidence interval of (6.3, 7.3), which of the following is an appropriate conclusion? a. the current study does provide significant evidence that the mean number of weekly hours has changed over the past year, since 6 falls outside the confidence interval. b. the current study does not provide significant evidence that the mean number of weekly hours has changed over the past year, since 6 falls outside the confidence interval. c. the current study does provide significant evidence that the mean number of weekly hours has changed over the past year, since 6 falls inside the confidence interval. d. the current study does not provide significant evidence that the mean number of weekly hours has changed over the past year, since 6 falls inside the confidence interval. e. you cannot draw a conclusion because the only way to reach a conclusion is to find the p - value of the test.

Explanation:

Step1: Recall confidence - interval concept

If the hypothesized value lies outside the confidence interval, we reject the null hypothesis. Here, the null hypothesis is that the mean has not changed (i.e., $\mu = 6$).

Step2: Check the position of 6

The 95% confidence interval is (6.3, 7.3) and the hypothesized value of $\mu = 6$ lies outside this interval. So, we reject the null hypothesis.

Answer:

A. The current study does provide significant evidence that the mean number of weekly hours has changed over the past year, since 6 falls outside the confidence interval.