Based on a random sample, is there a difference in the mean age among the 3 education levels: More than High School, High School, or Less than High school? To answer this statistical question, which statistical procedure should be/should not be used and why? Respond and explain why. (The typical format for each answer is "yes/no, [reason why each works or does not work]") The hypothesis test to compare two proportions? Explain Hypothesis test to compare two independent means? Explain. Hypothesis test for Paired Comparisons? Explain. ANOVA? Explain.
Question
Based on a random sample, is there a difference in the mean age among the 3 education levels: More than High School, High School, or Less than High school?
To answer this statistical question, which statistical procedure should be/should not be used and why?
Respond and explain why. (The typical format for each answer is "yes/no, [reason why each works or does not work]")
The hypothesis test to compare two proportions? Explain Hypothesis test to compare two independent means? Explain. Hypothesis test for Paired Comparisons? Explain. ANOVA? Explain.
Solution
The hypothesis test to compare two proportions? No, this test is not appropriate because we are not comparing proportions, but rather the mean age across three different education levels.
Hypothesis test to compare two independent means? No, this test is not appropriate because we are comparing more than two groups. This test is designed for comparing the means of two independent groups, not three.
Hypothesis test for Paired Comparisons? No, this test is not appropriate because our groups (education levels) are independent, not paired. Paired comparisons are used when the observations are dependent, such as before-and-after observations on the same subjects.
ANOVA? Yes, this is the appropriate test to use. ANOVA (Analysis of Variance) is designed to compare the means of three or more independent groups, which is exactly what we are doing in this case. It will allow us to determine if there is a statistically significant difference in the mean age among the three education levels.
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