Question

# Test the claim that the mean GPA of night students is larger than 3.4 at the...

Test the claim that the mean GPA of night students is larger than 3.4 at the 0.10 significance level.

The null and alternative hypothesis would be:

H0:p=0.85H0:p=0.85
H1:p≠0.85H1:p≠0.85

H0:μ≥3.4H0:μ≥3.4
H1:μ<3.4H1:μ<3.4

H0:p≥0.85H0:p≥0.85
H1:p<0.85H1:p<0.85

H0:p≤0.85H0:p≤0.85
H1:p>0.85H1:p>0.85

H0:μ=3.4H0:μ=3.4
H1:μ≠3.4H1:μ≠3.4

H0:μ≤3.4H0:μ≤3.4
H1:μ>3.4H1:μ>3.4

The test is:

two-tailed

left-tailed

right-tailed

Based on a sample of 75 people, the sample mean GPA was 3.41 with a standard deviation of 0.03

The test statistic is:  (to 2 decimals)

The p-value is:  (to 2 decimals)

Based on this we:

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

Solution:

The null and alternative hypothesis is,

Ho:  3.4

Ha:  3.4

This a right (One) tailed test.

The test statistics,

t =( - )/ (s / n)

= ( 3.41 - 3.4 ) / ( 0.03 / 75 )

= 2.89

P-value = 0.002

Since, P-value = 0.00 < 0.10, Reject the null hypothesis.

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