# 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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