Question

Exercise 10-3

A sample of 35 observations is selected from a normal population. The sample mean is 26, and the population standard deviation is 4. Conduct the following test of hypothesis using the .05 significance level.

H0 : μ ≤ 25

H1 : μ > 25

(a)	Is this a one- or two-tailed test?
	"Two-tailed"-the alternate hypothesis is different from direction. "One-tailed"-the alternate hypothesis is greater than direction.

(b)	What is the decision rule? (Round your answer to 2 decimal places.)

(Click to select)Do not rejectReject 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 25.

(e)	What is the p-value? (Round your answer to 4 decimal places.)

p-value

Answer 1

Solution :

Given that,

Population mean = = 25

Sample mean = = 26

Population standard deviation = = 4

Sample size = n = 35

Level of significance = = 0.05

a)

This is a right tailed test.

"One-tailed"-the alternate hypothesis is greater than direction.

b)

Critical value ,

Z_c = 1.64

Reject Ho if z > Z_c

The test statistics,

Z =( - )/ (/n)

= ( 26 - 25 ) / 4/ 35)

= 1.48

The value of test statastic is 1.48

d)

Snice, It is observe that , z = 1.48 < Z_c = 1.64 , It is concluded that do not reject null hypothesis.

Therefore , sufficient evidence to conclude that the population mean is greater than 25.

e)

p-value = 1 - P(Z < z)

= 1 - 0.9306

= 0.0694