A Sample of 12 Radon Detectors of a Certain Type $$\begin{array} { r r r r r r } 104.3 & 89.6 & 89.9 & 95.6 & 95.2 & 90.0 \\98.8 & 103.7 & 98.3 & 106.4 & 102.0&91 .1\end{array}$$

Essay

A sample of 12 radon detectors of a certain type was selected, and each was exposed to 100 pCi/L of radon. The resulting readings were as follows: $$\begin{array} { r r r r r r } 104.3 & 89.6 & 89.9 & 95.6 & 95.2 & 90.0 \\98.8 & 103.7 & 98.3 & 106.4 & 102.0&91 .1\end{array}$$
a. Does this data suggest that the population mean reading under these conditions differs from 100? State and test the appropriate hypotheses using $\alpha$
=.05
b. Suppose that prior to the experiment, a value of $\sigma$
=7.5 had been assumed. How many determinations would then have been appropriate to obtain $\beta = .10$
for the alternative $\mu = 95 ?$