(10 pts) At the College of Weber City, an SRS of 25 students was asked how much time they spent per week in the library. The sample average was 16 hours, and the population standard deviation is 1 hour. Provide a 98% confidence interval for the mean time spent in the library.
See p. 371. α = 0.05, μ_{0}
= 200 lbs., σ = 3 lb, x̅ = 198 lbs and n = 9. Thus H_{0}
is μ = 200 lbs and H_{a} is μ ≠ 200 lbs. Then z = ( x̅
- μ_{0}) / (σ /√n ) = -2, so
P-value = 2 · P(Z ≥ |-2|) = 2*P(Z ≤ -2) = 2 · 0.0228 = 0.0456
< α = 0.05. Thus we reject the null hypothesis, i.e.,
that the average weight of hogs on a certain diet is 200 lbs.