6.9. In response to the statement "A preschool child is likely to suffer if his or her mother works," the response categories (Strongly agree. Agree. Disagree, Strongly disagree) had counts (91, 385, 421, 99) for responses in a GSS. To treat this ordinal variable as quantitative, we assign scoresto the categories. For the scores (2,1, -1, —2), which treat the distance between Agree and Disagree as twice the distance between Strongly agree and Agree or between Disagree and Strongly disagree, software reports:

N Mean Std Dev Std Err 996 -0.052 1.253 0.0397

(a) Set up null and alternative hypotheses to test whether the population mean response differs from the neutral value, 0.

(b) Find the test statistic and P-value. Interpret, and make a decision about//o, using a = 0.05.

(c) Based on (b), can you "accept" Hq: fx = 0?

Why or why not?

(d) Construct a 95% confidence interval for /x.

Show the correspondence between whether 0 falls in the interval and the decision about Hq.