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.
For a known standard deviation a confidence level of 99% we may consider Z=2.576. So, the confidence interval would be calculated by: [tex]mean-Z\frac{standard~deviation}{ \sqrt{number~of~students~in~the~group} } [/tex] , [tex]mean+Z\frac{standard~deviation}{\sqrt{number~of~students~in~the~group} } [/tex] ⇔ ⇔ [tex]15.3-2.576 \frac{8.5}{ \sqrt{463} } [/tex] , [tex]15.3+2.576 \frac{8.5}{ \sqrt{463} } [/tex] ⇔ ⇔ [tex]15.3-1.018 [/tex] , [tex]15.3+1.018 [/tex] ⇔ ⇔ [tex]14.282 [/tex] , [tex]16.318 [/tex] 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.
