8. A manufacturer has developed a new fishing line, which the company claims has a mean breaking strength of 15 kilograms with a standard deviation of 0.5 kilogram. To test the hypothesis that μ = 15 kilograms against the alternative that μ < 15 kilograms, a random sample of 50 lines will be tested. The critical region is defined to be x̄ < 14.9.
(a) Find the probability of committing a type I error when H0 is true.
(b) Evaluate β for the alternatives μ = 14.8 and μ = 14.9 kilograms.
11. The grades of a class of 9 students on a midterm report (x) and on the final examination (y) are as follows:
77 50 71 72 81 94 96 99 67 y 82 66 78 34 47 85 99 66 68
(a) Estimate the linear regression line.
(b) Estimate the final examination grade of a student who received a grade of 85 on the midterm report.
(d) Evaluate s^2.
(e) Construct a 95% confidence interval for β1.