Question #178389

The Head of the Math Department announced that the mean score of Grade 9 students in the first periodic examination in Mathematics was 89 and the standard deviation was 12. One student who believed that the mean score was less than this, randomly selected 34 students and computed their mean score. She obtained a mean score of 85. At 0.01 level of significance, test the student’s belief.

Expert's answer

We have that:

The hypothesis test is left-tailed.

Since the population standard deviation is known and the sample size is large (>30) we use the *z*-test.

The critical value for is *Z*_{0.01 }= –2.33

The critical region is *z *< –2.33

Test statistic:

Since –1.94 > –2.33 thus the *Z*_{test}_{ }does not fall in the rejection region we fail to reject the null hypothesis.

There is no sufficient evidence to support the student’s belief. We are 99% confident to conclude that the mean score of Grade 9 students in the first periodic examination in Mathematics is 89.

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