# Conclusion since p value 005 we do not reject h there

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Conclusion: Since p -value > 0.05, we do not reject 0 H . There is insufficient evidence, at 5% level of significance, to conclude that 22000 . Example 8.10 : The security department of a factory wants to know whether or not the true average time required by the night guard to walk his round is 30 minutes. If, in a random sample of 100 rounds, the night guard averaged 30.8 minutes with a standard deviation of 3.8 minutes, determine the minimum value of the level of significance to claim that the true average time is not 30 minutes? Solution : Unbiased estimates for population mean and population variance, 2 2 100 sample variance 99 100 = 30.8 14.5 3 8 .8 59 9 1 9 3.819 x s s Let X be the time required by the night guard to walk his round. To test 0 1 : 30 : 30 H H at % level of significance Test Statistics: Under 0 H , by Central Limit Theorem, 2 3.8191 ~ N 30, approximately 100 X and test statistic, 2 100 ~ N(0,1) 3.8191 100 X Z

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