The American Economic Review (March 2008) published research on how the gender mix of a U.S. legislator's children can influence the legislator's votes in Congress. Specifically, the researcher investigated how having daughters influences voting on women's issues. The American Association of University Women (AAUW) uses voting records of each member of Congress to compute an AAUW score, where higher scores indicate more favorable voting for women's rights. The researcher modeled AAUW score (y) as a function of the number of daughters (x) a legislator has. Data collected for the 434 members of the 107th Congress were used to fit the straight-line model, E(y) = β0 + β1x.
a. If it is true that having daughters influences voting on women's issues, will the sign of β1 be positive or negative? Explain.
b. The following statistics were reported in the article: 1 = .27 and s1= .74. Find a 95% confidence interval for β1.
c. Use the result, part b, to make an inference about the model.