The data shown in the table represent the GPAs of randomly selected freshmen, so

Question

The data shown in the table represent the GPAs of randomly selected freshmen, sophomores, juniors, and seniors. At alpha = 0.05, can you conclude that there is a difference in the means of the GPAs? Assume that the populations of GPAs are normally distributed and that the population variances are equal. Use technology to test the claim. Identify the claim and state H_0 and H_a. Enter the data. Perform the ANOVA test to find the P-value. Decide whether to reject the null hypothesis. Interpret the decision in the context of the claim.

Explanation / Answer

Sol:

null hypothesis:All group means are equal

H0:freshmen= sophomores= juniors =seniors

Alternative hypothesis

Ha: Atleast one of the means are different.

Ha is cliam

decision

if p<0.05 reject null hypothesis

if p>0.05 fail to reject null hypothesis

here

p=0.2801

p>0.05

fail to reject null hypothesis

Accept null hypothesis

conclusion:

there is no sufficient evidence at 5% level of significanc to support the claim and conclude that there is a diff in the means of GPA

THERE IS NO DIFF IN THE MEANS OF GPA OF THE 4 GROUPS

Anova: Single Factor SUMMARY Groups Count Sum Average Variance freshmen 7 18.86 2.694286 0.219929 sophomores 10 30.55 3.055 0.132294 juniors 9 25.68 2.853333 0.130225 seniors 8 23.68 2.96 0.1154 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 0.584029 3 0.194676 1.33957 0.280101 2.922277 Within Groups 4.359821 30 0.145327 Total 4.94385 33

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