Question

Based on a random sample of 52 full-time college students, a 99% confidence interval for the mean number of hours that full-time college students sleep per night is [6.73, 7.67] hours.

Suppose you wanted to do a hypothesis test at the 1% significance level to see if the number of hours college students sleep is different than 7 hours.

Write the null and alternative hypotheses for this test. You may use words for the hypothesis statements rather than trying to use the equation editor in Canvas - for example use "mu" for the population mean.

Answer 1

The null hypothesis for the test would be that the mean number of hours that full-time college students sleep per night is 7 hours (H0: μ = 7), while the alternative hypothesis would be that the mean is not 7 hours (H1: μ ≠ 7).

Step-by-step explanation:

For the hypothesis test to determine if the number of hours college students sleep is different from 7 hours, the null hypothesis (H0) and the alternative hypothesis (H1) would be formulated as follows:

• H0: μ = 7 (The mean number of hours that full-time college students sleep per night is 7 hours)
• H1: μ ≠ 7 (The mean number of hours that full-time college students sleep per night is not 7 hours)

Since the confidence interval of [6.73, 7.67] hours includes the hypothesized mean of 7 hours, we would expect the null hypothesis to not be rejected at the 1% significance level, assuming the test statistic falls within the range set by the confidence interval.