Question

Test the claim that the mean GPA of night students is significantly different than 3.2 at the 0.01 significance level.

The null and alternative hypothesis would be:

A) H0:μ=3.2H0:μ=3.2
H1:μ≠3.2H1:μ≠3.2

B) H0:μ=3.2H0:μ=3.2
H1:μ<3.2H1:μ<3.2

C) H0:p=0.8H0:p=0.8
H1:p≠0.8H1:p≠0.8

D) H0:μ=3.2H0:μ=3.2
H1:μ>3.2H1:μ>3.2

E) H0:p=0.8H0:p=0.8
H1:p>0.8H1:p>0.8

F) H0:p=0.8H0:p=0.8
H1:p<0.8H1:p<0.8

The test is:

A) right-tailed

B) two-tailed

C) left-tailed

Based on a sample of 25 people, the sample mean GPA was 3.15 with a standard deviation of 0.03

The test statistic is:___ (to 2 decimals)

The positive critical value is: ___ (to 2 decimals)

Based on this we:

A) Fail to reject the null hypothesis

B) Reject the null hypothesis

Answer 1

Solution :

Given that ,

= 3.2  

= 3.15

= 0.03

n = 25

The null and alternative hypothesis is ,

H₀ :   = 3.2

H₁ :    3.2

This is the two tailed test .

Test statistic = z

= ( - ) / / n

= ( 3.15 - 3.2) / 0.03 / 25

= -8.33

The test statistic IS : -8.33

= 0.01

Z = Z_0.01 = +/-2.58

The positive critical value is : 2.58

-8.33 < 2.58

Test statistic < Critical value

B) Reject the null hypothesis .