Question: Consider the breaking strength data of Table 3.6. Notice that the normal plot of these data given as Figure 3.18 is reasonably linear. It may thus be sensible to suppose that breaking strengths for generic towel of this type (as measured by the students) are adequately modeled as normal. Under this assumption,

1. Make and interpret \(95 \%\) two-sided and one-sided confidence intervals for the mean breaking strength of generic towels (make a one-sided interval of the form \((\#, \infty))\).
2. Make and interpret \(95 \%\) two-sided and one-sided prediction intervals for a single additional generic towel breaking strength (for the one-sided interval, give the lower prediction bound).
3. Make and interpret \(95 \%\) two-sided and one-sided tolerance intervals for \(99 \%\) of generic towel breaking strengths (for the one-sided interval, give the lower tolerance bound).
4. Make and interpret \(95 \%\) two-sided and one-sided confidence intervals for \(\sigma\), the standard deviation of generic towel breaking strengths.
5. Put yourself in the position of a quality control inspector, concerned that the mean breaking strength not fall under \(9,500 \mathrm{~g}\). Assess the strength of the evidence in the data that the mean generic towel strength is in fact below the \(9,500 \mathrm{~g}\) target. (Show the whole five-step significance-testing format.)
6. Now put yourself in the place of a quality control inspector concerned that the breaking strength be reasonably consistent-i.e., that $\sigma$ be small. Suppose in fact it is desirable that o be no more than \(400 \mathrm{~g} .\) Use the significance testing format and assess the strength of the evidence given in the data that in fact $\sigma$ exceeds the target standard deviation.

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