A sample of 60 observations is selected from a normal population. The sample mean is 37, and the population standard deviation is 8.
Conduct the following test of hypothesis using the 0.10 significance level.
H0 : μ ≤ 36
H1 : μ > 36
a. Is this a one- or two-tailed test?
One-tailed test or Two-tailed test
b. What is the decision rule? (Round the final answer to 3 decimal places.)
(Reject or Accept) H0 and (accept or reject H1 when z > _______ .
c. What is the value of the test statistic? (Round the final answer to 2 decimal places.)
Value of the test statistic: _________
d. What is your decision regarding H0?
Reject or Do not reject H0.
There is (enough or not enough) evidence to conclude that the population mean is greater than 36.
e. What is the p-value? (Round the final answer to 4 decimal places.)
Solution
=
36
=37
=8
n = 60
This is the right tailed test .
The null and alternative hypothesis is ,
H0 :
< 36
Ha :
> 36
Test statistic = z
= (
-
) /
/
n
= (37-36) / 8 /
60
= 0.97
Test statistic = z = 0.97
The critical value = 1.282
P(z > 0.97 ) = 1 - P(z < 0.97) = 1 - 0.8340
P-value =0.166
= 0.10
P-value >
0.166 > 0.10
Fail to reject the null hypothesis .
There is insufficient evidence to conclude that the population mean is greater than 36
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