Question

Test the claim that the mean GPA of night students is smaller than 3.1 at the 0.005 significance level. You believe the population is normally distributed, but you do not know the standard deviation.

The null and alternative hypothesis would be:

H0:μ≥3.1
H1:μ<3.1

H0:p≥0.775H0
H1:p<0.775H1

H0:p=0.775H0
H1:p≠0.775H1

H0:μ=3.1H0
H1:μ≠3.1H1

H0:μ≤3.1H0
H1:μ>3.1H1

H0:p≤0.775H0
H1:p>0.775H1

The test is:

left-tailed

right-tailed

two-tailed

Based on a sample of 20 people, the sample mean GPA was 3.06 with a standard deviation of 0.05

The test statistic is:  (to 2 decimals)

The p-value is:  (to 2 decimals)

Based on this we:

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

Answer 1

Sample size = n = 20

Sample mean = = 3.06

Standard deviation = s = 0.05

Claim: The mean GPA of night students is smaller than 3.1

The null and alternative hypothesis is

H0:μ≥3.1
H1:μ<3.1

Level of significance = 0.05

Here population standard deviation is unknown so we have to use t-test statistic.
Test statistic is

Degrees of freedom = n - 1 = 20 - 1 = 19

Critical value = 2.861    ( Using t table)

Test statistic | t | > Critical value we reject null hypothesis.

Conclusion:The mean GPA of night students is smaller than 3.1