A professor wants to estimate how many hours per week her students study. A simple random sample of 53 students had a mean of 19 hours of studying per week.

Construct a 90% confidence interval for the mean number of hours a student studies per week. Assume that the population standard deviation is known to be 33 hours per week. Round to two decimal places.

The 90% confidence interval for the mean number of hours a student studies per week is approximately (16.62, 21.38) hours. This means that we can be 90% confident that the true mean falls within this interval.

To construct the confidence interval, we can use the formula:

CI = X ± Z * (σ/√n),

where CI represents the confidence interval, X is the sample mean, Z is the Z-score corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size.

Given that the sample mean is 19 hours (X, the population standard deviation is 33 hours (σ), and the sample size is 53 (n), we can proceed with calculating the confidence interval.

Using a Z-score corresponding to a 90% confidence level (which is approximately 1.645), the formula becomes:

CI = 19 ± 1.645 * (33/√53).

Calculating the values:

CI = 19 ± 1.645 * (33/√53) ≈ 19 ± 2.88.

Rounding to two decimal places, the 90% confidence interval for the mean number of hours a student studies per week is approximately (16.62, 21.38) hours. This interval suggests that we can be 90% confident that the true mean number of hours falls within this range.

Learn more about standard deviation :

brainly.com/question/29115611

#SPJ11