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:

106.5 97.4

105.9

92.2

100.5 97.8 101.0 108.6

104.2

93.3

92.1

91.8

USE SALT

(a) Does this data suggest that the population mean reading under these conditions differs from 100? (Use alpha = 0.05 ) State the appropriate null and alternative hypotheses.

H_{0} / mu = 100

H_{a} / mu < 100

H_{0} / mu = 100

H_{a} / mu <= 100

O H_{0} / mu = 100

H_{a} / mu > 100 O H_{0} / mu = 100

H_{a} : mu ne100

Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)

t = boxed -3.85

P-value = 0.001

State the conclusion in the problem context.

O Do not reject the null hypothesis. There is sufficient evidence to conclude that the population mean reading under these conditions differs from 100 pCi/L.

Reject the null hypothesis. There is sufficient evidence to conclude that the population mean reading under these conditions differs from 100

pCi/L.

Reject the null hypothesis. There is not sufficient evidence to conclude that the population mean reading under these conditions differs from 100 pCi/L.

Do not reject the null hypothesis. There is not sufficient evidence to conclude that the population mean reading under these conditions differs from 100 pCi/L.

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(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 = 0.1 for the alternative mu = 95 (You will need to use the appropriate table in the Appendix of Tables to answer this question.) determinations