Question

A professor wants to estimate how many hours per week her students study. A simple random sample of 56 students had a mean of 20 hours of studying per week. Construct a 98% confidence interval for the mean number of hours a student studies per week. Assume that the population standard deviation is known to be 2 hours per week. Round to two decimal places.

Answer 1

To construct a 98% confidence interval for the mean number of hours a student studies per week, use the formula: Confidence Interval = sample mean ± z * (population standard deviation / √sample size).

Step-by-step explanation:

To construct a 98% confidence interval for the mean number of hours a student studies per week, we can use the formula: Confidence Interval = sample mean ± z * (population standard deviation / √sample size).

In this case, the sample mean is 20, the population standard deviation is 2, and the sample size is 56. The z-value for a 98% confidence level is 2.33. Plugging these values into the formula:

Confidence Interval = 20 ± (2.33 * (2 / √56))

Calculating the expression, we get:

Confidence Interval ≈ 20 ± 0.626

Rounding to two decimal places, the confidence interval is approximately (19.37, 20.63).

Therefore, we can say with 98% confidence that the mean number of hours a student studies per week falls between 19.37 and 20.63 hours.