Question

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?
	"One-tailed"-the alternate hypothesis is greater than direction. "Two-tailed"-the alternate hypothesis is different from direction.

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?
	Do not reject Reject

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

Answer 1

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