In Illinois, a random sample of 85 eighth grade students has a mean score of 265 with a standard deviation of 55 on a national

In Illinois, a random sample of 85 eighth grade students has a mean score of 265 with a standard deviation of 55 on a national mathematics assessment test. This test result prompts a state school administrator to declare that the mean score for that state’s eighth graders on the examination is more than 260. At, is there enough evidence to support the administrator’s claim?

Solution:

(a) The null and alternative hypotheses are:

This corresponds to a right-tailed test. The population variance is not known, but the sample size is big enough to use a Z-test.

(b) The Z-statistics is computed as:

(c) The p-value is computed as:

(d) Since the p-value found is greater than 0.04, we fail to reject the null hypothesis.

(e) We don’t have enough evidence to support the claim that the mean score is greater than 260, at the 0.04 significance level.

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