Question

A group of 463 first-year college students were asked, “About how many hours do you study during a typical week?” The mean response is 15.3 hours. Assume that the study time is normally distributed with a sample standard deviation of 8.5 hours. Construct a 99% confidence level interval for the mean study time of all first-year students.

Answer 1

For a known standard deviation a confidence level of 99% we may consider Z=2.576.
So, the confidence interval would be calculated by:

`mean-Z(standard~deviation)/( √(number~of~students~in~the~group) )` ,
`mean+Z(standard~deviation)/(√(number~of~students~in~the~group) )` ⇔
⇔
`15.3-2.576 (8.5)/( √(463) )` ,
`15.3+2.576 (8.5)/( √(463) )` ⇔
⇔
`15.3-1.018` ,
`15.3+1.018` ⇔
⇔
`14.282` ,
`16.318`
Considering the given data, with a 99% cofidence, it can be said that the true mean of hours of study in a typical week for first-year college students is between 14.282 and 16.318.