Question

A sample of 50 observations is selected from a normal population. The sample mean is 47, and the population standard deviation is 7. Conduct the following test of hypothesis using the 0.10 significance level:

H₀: μ = 48

H₁: μ ≠ 48

a. Is this a one- or two-tailed test?

(Click to select)  Two-tailed test  One-tailed test

b. What is the decision rule?

Reject H₀ and accept H₁ when z does not lie in the region

from  to.

c. What is the value of the test statistic? (Negative answer should be indicated by a minus sign. Round the final answer to 2 decimal places.)

Value of the test statistic           

d. What is your decision regarding H₀?

(Click to select)  Reject  Fail to reject  H₀

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

The p-value is             .

Answer 1

Solution :

= 47

=48

= 7

n = 50

a ) This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    = 48

Ha :     48

b ) The rejection region for this two-tailed test is R = {z:∣z∣>1.64

c )Test statistic = z

= ( - ) / / n

= (47-48 ) / 7 / 50

= −1.01

Test statistic = z = −1.01  

P-value =0.3124

= 0.10  

P-value <

0.3124 ≥ 0.10

d )Fail to reject the null hypothesis .

There is insufficient evidence to suggest that