Homework SourseA sample of 39 observations is selected from a normal popula
A sample of 39 observations is selected from a normal population. The sample mean is 31, and the population standard deviation is 5. Conduct the following test of hypothesis using the .05 significance level.
| A sample of 39 observations is selected from a normal population. The sample mean is 31, and the population standard deviation is 5. Conduct the following test of hypothesis using the .05 significance level. |
| H0 : ? ? 30 |
| H1 : ? > 30 |
Solution
(a)\"One-tailed\"-the alternate hypothesis is greater than direction.
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(b) Given a=0.05, the critical value is Z(0.05) =1.645 (from standard normal table)
Reject H0 and do not reject H1 when z > 1.64
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(c) test statistic:
Z=(xbar-mu)/(s/vn)
=(31-30)/(5/sqrt(39))
=1.25
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(d)Do not reject
There isinsufficient evidence to conclude that the population mean is greater than 30.
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(e) The p-value= P(Z>1.25) =0.1056 (from standard normal table)
