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A random sample of 85 students has a mean score of 265 with
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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?
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7 years ago.
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Expert:
SteveS
replied 7 years ago.
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Customer:
replied 7 years ago.
z(alpha) is 0.05, isn't the z score 1.96? i.e. 90%
Expert:
SteveS
replied 7 years ago.
z(alpha) = 1.96 for a twotailed test, z(alpha) = 1.645 for a onetailed test. In this problem, it's a onetailed test, so we use 1.645 as the z score. Either way, the conclusion remains the same.
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Customer:
replied 7 years ago.
Please forgive me, but a quick follow up...
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 7 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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