A sample of 37 observations is selected from a normal population. The sample mean is 29, and the population standard deviation is 5. Conduct the following test of hypothesis using the 0.05 significance level. |
H0 : μ ≤ 26 |
H1 : μ > 26 |
a. | Is this a one- or two-tailed test? | ||||
|
b. | What is the decision rule? (Round your answer to 3 decimal places.) |
(Click to select)RejectDo not reject H0, when z > |
c. | What is the value of the test statistic? (Round your answer to 2 decimal places.) |
Value of the test statistic |
d. | What is your decision regarding H0? | ||||
|
There is (Click to select)sufficientinsufficient evidence to conclude that the population mean is greater than 26. |
e. | What is the p-value? (Round your answer to 4 decimal places.) |
p-value |
H0: <= 26
Ha: > 26
a)
One tailed - the alternative hypothesis is greater than direction.
b)
Decision rule -
Reject H0 if z > 1.645
c)
Test statistics
z = - / / sqrt(n)
= 29 - 26 / 5 / sqrt(37)
= 3.65
d)
Since test statistics falls in rejection region , Reject H0
e)
There is sufficient evidence to conclude that population mean is greater than 26
p-value = P( Z > z)
= P( Z > 3.65)
= 0.0001
A sample of 37 observations is selected from a normal population. The sample mean is 29,...
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