Question

You have some friends who are doing a group project with you. The goal is to test H0 : u = 5 vs H1 : u > 5. They have to go, but before they leave they tell you what they have found. They have a sample mean = 4.8, a critical number x bar ( this would be x with a bar over it ) critical = 4.9, ( xc = 4.9 , where the underline should be on top of the

x .). They also tell you that n = 36 and σ = 1.1. They used some alpha, but they did not tell you what it is.

A). Do you reject the null hypothesis or not? Do you accept the alternative hypothesis? Why???

B) Find α.

C) Find the P-value.

Answer 1

a) As we are given the the sample mean of 4.8 which is less than 4.9, that is the critical mean value therefore the test is not significant here, and therefore we do not reject the null hypothesis here.

Therefore Do not reject null hypothesis here. We have sufficient evidence to support the alternative hypothesis here.

b) The level of significance here is computed as:

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we get here:

Therefore 0.7073 is the required alpha or level of significance here.

c) The p-value here is computed as: (for a sample mean of 4.8):

Getting it from the standard normal tables, we get here:

Therefore 0.8623 is the required p-value here.