In each of the following problems, the sample mean, the sample standard deviation, the sample size, and the confidence level are given. Assume the underlying population is normally distributed. Find the associated confidence interval for the population mean.
In each of the following problems, put the values in order from smallest to largest. (Note: There is no need to use a table or technology here. Use your knowledge of the t distribution and the Z distribution.)
During the manufacture of certain commercial windows and doors, hot steel ingots are passed through a rolling mill and flattened to a prescribed thickness. The machinery is set to produce a steel section 0.25 inch thick. Fourteen steel sections were selected at random and the thickness of each was recorded. The data are given in the table below.
Assume the underlying distribution of section thickness is normal.
a. Find a 99% confidence interval for the true mean steel section thickness.
b. As the rollers erode, the machine begins to produce steel sections that are too thick. Using your answer to part (a), is there any evidence to suggest the true mean steel section thickness is more than 0.25 inch? Justify your answer.
c. Use the methods described in Section 6.3, page 272, to check for any evidence of non-normality.