Question

Suppose we know the population variance σ 2 =1600, there is a random sample with x̄ =134, and the s ample size is n= 81.

a) Please do the following test and draw your conclusion using the critical region method. In the question, please choose α=0.05 . Hint: what kind of tests you are going to use, one sample Z test or one sample t test?

H 0: μ = 1 25 Vs H 1: μ ≠ 125

b) Please repeat the test, find the p-value and draw your conclusion based on p-value.

Answer 1

Solution :

= 125

=134

² = 1600

=40

n = 81

a ) This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :    = 125

H_a :     125

Test statistic = z

= ( - ) / / n

= (134-125) / 40 / 81

= 2.025

Test statistic = z = 2.02

The information provided, the significance level is α=0.05, and the critical value for a two-tailed test is z_c​=1.96

b ) P-value =0.0429

= 0.05  

P-value <

0.0429 < 0.05

Reject the null hypothesis .

There is sufficient evidence to suggest that