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# A random sample of 85 students has a mean score of 265 with

### Customer Question

A random sample of 85 students has a mean score of 265 with a standard deviation of 55 on a test. This test results in the state declaring the mean score is more than 260. At a=0.05, is there enough evidence to support the administators claim?
Submitted: 5 years ago.
Category: Homework
Expert:  SteveS replied 5 years ago.
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SteveS, MBA
Category: Homework
Satisfied Customers: 453
Experience: MBA from Top 5 US Business School, Tutoring Experience for Over Two Years
Customer: replied 5 years ago.
z(alpha) is 0.05, isn't the z score 1.96? i.e. 90%
Expert:  SteveS replied 5 years ago.
z(alpha) = 1.96 for a two-tailed test, z(alpha) = 1.645 for a one-tailed test. In this problem, it's a one-tailed test, so we use 1.645 as the z score. Either way, the conclusion remains the same.
Customer: replied 5 years ago.

If the null hypothesis H0: mean <= 260, and we cannot reject this, doesn't this provide evidence in favor of the admins claim?

Sorry, this seems to be going over my head a bit...
Expert:  SteveS replied 5 years ago.
No problem. The null hypothesis is the opposite claim of the administration's claim. The only way we can support the administration's claim is to reject the null hypothesis. Since we cannot reject the null hypothesis (mean<=260), we cannot support the administration's claim with 95% confidence that the mean > 260.

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