Question

A sample of 34 observations is selected from a normal population. The sample mean is 30, and the population standard deviation is 3. Conduct the following test of hypothesis using the 0.05 significance level:

H₀: μ = 31

H₁: μ ≠ 31

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

(Click to select)  One-tailed test  Two-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)  Fail to reject  Reject  H₀

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

The p-value is             .

Answer 1

Solution :

= 31

=30

=3

n = 34

a )This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    = 31

Ha :     31

b ) Test statistic = z

= ( - ) / / n

= (30-31) / 3 / 34

= -1.94

c )Test statistic = z = -1.94

The significance level is \alpha = 0.05 α=0.05, and the critical value for a two-tailed test is Zc​=1.96

it is observed that ∣z∣=-1.94 ≤ Zc​ ​=1.96, it is then concluded that the null hypothesis is not rejected

P-value = 2 * 0.0262 =0.0524

= 0.05  

d )P-value >

0.0524 > 0.05

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that