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 $\mu = 95 ?$

Question

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 $\mu = 95 ?$

Quizplus · Accepted Answer

The Answer of 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 $\mu = 95 ?$

A Sample of 12 Radon Detectors of a Certain Type 104.389.689.995.695.290.098.8103.798.3106.4102.091.1\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}104.398.8​89.6103.7​89.998.3​95.6106.4​95.2102.0​90.091.1​

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