Question

Test the claim that the mean GPA of night students is smaller than 3 at the...

Test the claim that the mean GPA of night students is smaller than 3 at the .10 significance level.

The null and alternative hypothesis would be:

H0:p=0.75H0:p=0.75
H1:p<0.75H1:p<0.75

H0:μ=3H0:μ=3
H1:μ<3H1:μ<3

H0:μ=3H0:μ=3
H1:μ≠3H1:μ≠3

H0:p=0.75H0:p=0.75
H1:p≠0.75H1:p≠0.75

H0:μ=3H0:μ=3
H1:μ>3H1:μ>3

H0:p=0.75H0:p=0.75
H1:p>0.75H1:p>0.75

The test is:

left-tailed

two-tailed

right-tailed

Based on a sample of 35 people, the sample mean GPA was 2.97 with a standard deviation of 0.08

The test statistic is:  (to 2 decimals)

The critical value is:  (to 2 decimals)

Based on this we:

• Reject the null hypothesis
• Fail to reject the null hypothesis

Solution:

a)

The null and alternative hypothesis would be:

H0: μ = 3
H1: μ < 3

b)

The test is:

left-tailed

c)

The test statistic t is

t =   = [2.97 - 3]/[0.08 /35] = -2.22

The test statistic is: -2.22

d)

d.f. = n - 1 = 35 - 1 = 34

= 0.10 given

For left tailed test ,

critical value is

The critical value is: -1.31

e)

Based on this we:

Reject the null hypothesis