Question

Consider the following situation: A sleep study collected data from a random sample of 40 college students and recorded the hours of sleep on a particular night for each student. The average hours of sleep for the students in this sample was 7.759 hours. It is known that the population standard deviation for nightly hours of sleep is 1.272 hours. Published data has indicated that the mean nightly hours of sleep for the general population is 8.125 hours. The sleep study wants to test if college students get less sleep than the general population.

Which of the following hypothesis tests would be appropriate in this situation?

Group of answer choices

t-test for population mean

z-test for population mean

z-test for population proportion

paired t-test

two-sample t-test for population mean differences

Answer 1

The appropriate hypothesis test in this situation would be a z-test for population mean.

Therefore, the correct answer is: option 'z-test for population mean'.

Step-by-step explanation:

Since the population standard deviation is known and the sample size is larger than 30, a z-test can be used.

The z-test allows us to compare the sample mean to the population mean and determine if there is a significant difference.

To perform the z-test, we would calculate the z-score using the formula z = (sample mean - population mean) / (population standard deviation / sqrt(sample size)).

We can then compare the z-score to the critical value from the z-table to determine if we reject or fail to reject the null hypothesis.

Therefore, the appropriate hypothesis test in this situation would be a z-test for population mean.