Reconsider the filtration rate-moisture content data introduced in Example 12.6 (see also Example 12.7).
a. Compute a 90% CI for β1 + 125 β1, true average moisture content when the filtration rate is 125.
b. Predict the value of moisture content for a single experimental run in which the filtration rate is 125 using a 90% prediction level. How does this interval compare to the interval of part (a)? Why is this the case?
c. How would the intervals of parts (a) and (b) compare to a CI and PI when filtration rate is 115? Answer without actually calculating these new intervals.
d. Interpret the hypotheses H0: β0 + 125 β1 = 80 and Ha: β0 + 125 β1, 80, and then carry out a test at significance level .01.