Question

Give an estimate of the mean hardness that you would expect after 37 and 41 hours; and a 85% confidence interval for each estimate. which confidence interval is wider and why is it wider?

Answer 1

The predicted value of hardness at 37 hours is 243.87 and an 85% confidence interval for the mean hardness is (242.12, 245.61). At 41 hours, the predicted hardness is 252 and an 85% confidence interval for mean hardness is (249.83, 254.18). The confidence interval for X is equals to 41 which is wider because the value 41 is farther away from the sample mean X than is 37. As an outcome, the standard error for the prediction is larger.