Question

Consider the following: H_0: µ = 22 H_a: µ ≠ 22

A sample of size 75 provided a sample mean of 25.1. The population standard deviation is 10.

a) Compute the value of the test statistic

b) What is the associated p-value?

c) Using α = 0.01, what is your conclusion? Enter either "reject" or "fail to reject" without the quotes for what to do with the null hypothesis.

Answer 1

this is the two tailed test .  

The null and alternative hypothesis is ,

H₀ :   = 22

H_a :     22

Test statistic = z

= ( - ) / / n

= (25.1-22) / 10 / 75

=2.68

P(z > 2.68) = 1 - P(z < 2.68) = 1-0.9963=0.0037

P-value =2*0.0037=0.0074

= 0.01

P-value <

Reject the null hypothesis .