Question

a professor wants to estimate how many hours per week her students study. a simple random sample of 74 students had a mean of 20 hours of studying per week. construct a 99% confidence interval for the mean number of hours a student studies per week. assume that the population standard deviation is known to be 3.5 hours per week. round to two decimal places.

Answer 1

99% confidence Interval for the mean number of hours a student studies per week is (21.0208,18.9792)

Given:

mean x = 20

standard deviation σ = 3.5

sample size n = 78

z score for 99% = 2.576

Interval = x±z*s/$\sqrt{n}$

= 20±2.576*3.5/$\sqrt{78}$

= 20±2.576*0.39629

= 20±1.0208

Interval = (21.0208,18.9792)

Therefore 99% confidence Interval for the mean number of hours a student studies per week is (21.0208,18.9792).

Learn more about the confidence interval here:

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