Question

A sample of 148 college students reports sleeping an average of 6.85 hours on weeknights. The sample size is large enough to use the normal distribution, and a bootstrap distribution shows that the standard error is SE = 0.175. Use a normal distribution to construct and interpret a 95% confidence interval for the mean amount of weeknight sleep students get at this university. Use two decimal places in your answer.

Answer 1

The 95% confidence interval for the mean amount of weeknight sleep that college students get at this university is calculated to be (6.51, 7.19) hours.

Step-by-step explanation:

To construct a 95% confidence interval for the mean amount of weeknight sleep that college students get at this university, we use the sample mean, standard error, and the z-score that corresponds to the desired confidence level. Since the sample size is large, the central limit theorem allows us to use the normal distribution.

For a 95% confidence interval, the z-score (from a standard normal distribution table) is approximately 1.96. The standard error (SE) is given as 0.175. The confidence interval is calculated as:

Confidence interval = sample mean ± (z-score * standard error)
= 6.85 ± (1.96 * 0.175)
= 6.85 ± 0.343

Therefore, the confidence interval is (6.51, 7.19). This means we are 95% confident that the true mean amount of weeknight sleep that college students get at this university is between 6.51 and 7.19 hours.