A machine that makes hose fittings is set for a tolerance of \(0.25 \mathrm{~cm}\) (i.e., the standard deviation) and a mean diameter of \(12 \mathrm{~cm}\). A random sample of 12 fittings (in \(\mathrm{cm}\) ) is given in Table 4.7.

Find and interpret \(99 \%\) confidence intervals for both the population mean diameter and the population variance of the hose fittings.

Table 4.7

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Mean Diameter (in Centimeters) for a Random Sample of 12 Hose Fittings 12.24 12.64 12.15 12.36 12.60 12.02 12.18 11.95 11.95 12.08 12.23 11.89