GSS 2014 respondents were asked, “Some people say the following things are impor
ID: 3179554 • Letter: G
Question
GSS 2014 respondents were asked, “Some people say the following things are important for being truly American. Others say they are not important. How important do you think each of the following is—to be a Christian?” Responses were measured on a 4-point scale: 1=very important, 2=fairly important, 3=not very important, 4=not important at all. Those with a high school degree had an average score of 2.35 (s = 1.21, n = 189). Those with a bachelor’s degree had an average score of 3.05 (s = 1.05, n = 61). Test your null hypothesis with a one-tailed test; = .05. What do you conclude about the difference in attitudes between high school and bachelor’s degree graduates?
Explanation / Answer
Solution:-
1 = 2.35, s1 = 1.21, n1 = 189
2 = 3.05, s2 = 1.05, n2 = 61
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: 1 = 2
Alternative hypothesis: 1 < 2
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the mean difference between sample means is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
S.E = sqrt[(s12/n1) + (s22/n2)]
S.E = 0.1607
DF = 115.67
D.F = 116 (By using calculator)
t = [ (x1 - x2) - d ] / SE
t = - 4.356
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.
The observed difference in sample means produced a t statistic of - 4.356. We use the t Distribution Calculator to find P(t < - 4.356) = 0.000014
Interpret results. Since the P-value (0.000014) is less than the significance level (0.05), we have to reject the null hypothesis.
From the above test we have sufficient evidence that score of bachelor’s degree graduates is greater than the score of high school.
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