Question: Losen, Cahoy, and Lewis measured the lengths of some spanner bushings of a particular type purchased from a local machine supply shop. The lengths obtained by one of the students were as follows (the units are inches):

1.1375,1.1390,1.1420,1.1430,1.1410,1.1360

1.1395,1.1380,1.1350,1.1370,1.1345,1.1340

1.1405,1.1340,1.1380,1.1355

1. If you were to, for example, make a confidence interval for the population mean measured length of these bushings via the formulas in Section 6.3, what model assumption must you employ? Make a probability plot to assess the reasonableness of the assumption.
2. Make a \(90 \%\) two-sided confidence interval for the mean measured length for bushings of this type measured by this student.
3. Give an upper bound for the mean length with \(90 \%\) associated confidence.
4. Make a \(90 \%\) two-sided prediction interval for a single additional measured bushing length.
5. Make a \(95 \%\) two-sided tolerance interval for \(99 \%\) of additional measured bushing lengths.
6. Consider the statistical interval derived from the minimum and maximum sample values namely, (1.1340, 1.1430). What confidence level should be associated with this interval as a prediction interval for a single additional bushing length? What confidence level should be associated with this interval as a tolerance interval for \(99 \%\) of additional bushing lengths?

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