# The rejection region will be 2 calc z z due to

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The rejection region will be 2 calc z z . (Due to symmetry) (d) Conclusion After we have computed the value of the test statistic using the sample data, we have to make conclusion of our finding. If the value of the test statistics lies in the critical region, we reject 0 H . There is sufficient evidence to conclude that ………….(write the statement of 1 H in context) . If the value of the test statistics does not lie in the critical region, we do not reject 0 H .There is insufficient evidence to say that ……(write the statement of 1 H in context). Example 8.2 : Experience has shown that the scores obtained in a particular test are normally distributed with mean score 70 and variance 36. When the test is taken by a random sample of 36 students, the mean score is 68.5. Is there sufficient evidence, at 3% level, to conclude that these students have not performed as well as expected? Solution : Let X denote the scores obtained by a randomly chosen student Given ~ N(70,36) X , n 36 T o test 0 1 : 70 : 70 H H at 3% level of significance. T est Statistic: Under 0 H , 36 ~ N 70, 36 X and test 70 means that the students have not performed as well as expected. 0 z Critical region z 0 2 z 2 Critical region Critical region 2 2 z z

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