The GSS 2014 respondents in the U.S. were asked, "How important do you think that being a Christian is for being truly American?" Responses were measured on a 4-point scale: 1=very important, 2=fairly important, 3=not very important, 4=not important at all. We will treat this variable as continuous and interval/ratio. Those with a high school diploma 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). We will treat those with a high school diploma as group 1, and those with a bachelor’s degree as group 2. We want to know: Do those with a high school diploma have a lower average score on this measure than those with a bachelor’s degree? That is, are those with a high school diploma more likely than those with a bachelor’s degree to think it’s very important to be a Christian in order to be truly American?
Question 1: What is the critical value of the test statistic for our test of the null hypothesis at the .01 level of significance (report 3 decimal places)?
Question 2: Based on your calculated and critical values of the test statistic, what is your decision about the null hypothesis?
A. Accept the null hypothesis
B. Fail to reject the null hypothesis
C. Reject the null hypothesis
D. Too little information to determine