The governor of Stretford prison has a biographical record of all inmates. The mean age of all inmates is 22, with a standard deviation of 7.5. The prison governor suspects that the 100 interviewees were not chosen at random. The mean age of the interviewees chosen was 20. Can the government use this finding to cast doubt on the sampling method of the survey? Use an alpha of .05 Remember to outline each stage of the test.
How do you solve this Hypothesis test?
H_0: The mean age is 22.
H_A: The mean age is less than 22 (one-sided test) OR the mean age is not equal to 22 (two-sided test)
Z = (x-mu)/(sigma/sqrt(n)) = (20-22)/(7.5/10) = -2.667
Compare Z-statistic to quantiles of normal distribution and you'll see that the null hypothesis should be rejected at the alpha=0.05 level.
(for alpha=0.05 Z is 1.96 for 2-sided test and ? for 1-sided test)
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