Question

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

Test the claim that the mean GPA of night students is significantly different than 3.2 at the 0.05 significance level.

The null and alternative hypothesis would be:

H0:μ≥3.2H0:μ≥3.2
H1:μ<3.2H1:μ<3.2

H0:μ≤3.2H0:μ≤3.2
H1:μ>3.2H1:μ>3.2

H0:p=0.8H0:p=0.8
H1:p≠0.8H1:p≠0.8

H0:p≤0.8H0:p≤0.8
H1:p>0.8H1:p>0.8

H0:μ=3.2H0:μ=3.2
H1:μ≠3.2H1:μ≠3.2

H0:p≥0.8H0:p≥0.8
H1:p<0.8H1:p<0.8

The test is:

right-tailed

two-tailed

left-tailed

Based on a sample of 25 people, the sample mean GPA was 3.19 with a standard deviation of 0.08

The p-value is:  (to 2 decimals)

Based on this we:

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

The researcher wants to test the claim that the mean GPA of night students is significantly different than 3.2 at the 0.05 significance level.

The null and alternative hypothesis would be:

H0:μ=3.2
H1:μ≠3.2

The test is two-tailed.

It is given that based on 25 people (n) , the sample mean GPA was 3.19 with a standard deviation (s) of 0.08

The test statistic is given by,

Since, the test is a two-tailed, so the absolute test statistic is |t| = |-0.625| = 0.625.

The degrees of freedom (df) = n – 1 = 25 – 1 = 24

Using the t-table and the degrees of freedom (24), the p-value is,

Therefore, the p-value is 0.54.

Since, the p-value (0.54) is greater than the significance level 0.05, so the decision is fail to reject the null hypothesis.

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