Question

Radon detectors of a certain brand were tested for their accuracy. A sample of 12 radon detectors was picked and each was exposed to 100 pCi/L of radon. The resulting readings were as follows: 103.6, 88.9, 89.2, 94.9, 94.5, 89.3, 98.1, 103.0, 97.6, 105.7, 101.3, 90.4. At significance level 0.02, does this data suggest that the true mean reading under these conditions differs from 100?

Answer 1

Solution :

Given that samplesize n =12

To test the claim that, True mean reading under these conditions differs from 100.

Null hypothesis Vs

Alternative hypothesis

Using the given data, we will find the sample mean and sample standard deviation and use it to find test statistics.

So using Excel command as =Average() and =STDEV() we get ,sample mean = 96.375 and sample sd = 6.11

As here we found sample sd, we wil use T -test .

Test statistics :

Now to find critical value, we are given that level of significance alpha = 0.02

Using Statistical table , we get critical values as, +/-2.33

Decision rule: Reject Ho ,if |Test statistics| > |critical value| otherwise fail to reject Ho.

So as here |test statistics| = 2.06 is less than |critical value|=2.33 , we fail to reject Ho.

Conclusion : At 0.02 level of significance, we can say that this data does not suggest that the true mean reading under these conditions differs from 100.