Question

Side Note:Data for part 2 from the 2017 Current Population Survey shows a sample of 18 to 30 year old people who have either Grade 12 level of education or people with ONLY 1 year of college. The data also contains last year’s total personal income, which are in thousands of dollars, so 3 means $3,000. Please work with the smaller numbers below.

1. The data shows that for those 364 persons with only a high school education, who have positive total income, average total personal income (in thousands of dollars) was 19.73 with a standard deviation of 19.08. While for those 205 persons with ONLY 1 year of college but with positive total personal income, average total personal income was 15.66 (in thousands of dollars) with a standard deviation of 15.97. Using the t-test and the 1% significance level, test the hypothesis that average personal income from those with high school education and those with ONLY 1 year of college are the same. You do NOT need to adjust for small sample sizes.

Answer 1

Independent two samples t test would be appropriate in this situation; we want to test if the average personal income from those with high school education and those with ONLY 1 year of college are the same ie. μ The null and alternative hypothesis would be (The null hypothesis states that a population parameter is equal to a hypothesized value, and the alternative hypothesis states that a population parameter is smaller, greater, or different than the hypothesized value in the null hypothesis) We have, n1 364 persons with only a high school education, who have positive total income, average total personal income was x1 19.73 (in thousands of dollars) with a standard deviation of s1- 19.08 n2 205 persons with ONLY 1 year of college but with positive total personal income, average total personal income was x2-15.66 (in thousands of dollars) with a standard deviation of s2 15.97 The test statistic is given by, 19.73-15.66 19.082 15.972 364 205 = 2.716819484 To Calculate critical t value, α = 0.01 (1% significance level), t has n1 + n2-2 = 364 + 205-2 = 567 degrees of freedom and this is two tailed test (Since H1 with sign) using T.INV.2T(0.01,567) excel function we can get critical t value So, critical t 2.584528011 Since t > critical t, we reject null hypothesis at 1% level of significance i.e. we accept alternative hypothesis H1: μ1 μ2 the two population means are not equal

rejection region a/2 0.005/ rejection region a/2 0.005 2.58 2.58 2.71 Hence, the average personal income from those with high school education and those with ONLY 1 year of college are not same.