Since 1935. the Gallup Organization has polled the U.S. public on a number of po
ID: 3229909 • Letter: S
Question
Since 1935. the Gallup Organization has polled the U.S. public on a number of political, economic, social, and lifestyle issues. One social issue that has received repeated attention is the public's perception of gender differences. In March 2017. Gallup polled United States residents on whether they perceived certain personality characteristics as more true of men or women. The table below provides the percentages of men and women who judged the characteristic easy-going as more true for one gender than the other. Perform a goodness-of-fit test (i.e., a one-sample chi-square test) to determine whether men are more likely to believe that one gender is more easy-going than the other. (a) From the table it appears that men are more likely to believe that women are more easy-going than men. Why can't you rely solely on the percentages reported to infer that this is in fact the case for the general population of all male residents in the U.S. (i.e., why must you perform an inferential test here)? Explain in your own words, not the texts. (b) Set up your null and alternative hypotheses for the goodness-of-fit test. State these hypotheses in words. (c) What is your decision rule for this test? Make sure that you indicate the number of degrees of freedom involved here.Explanation / Answer
Null hypothesis : The values are independent
Alternate hypothsis : the two value catagories are related
sum = 5.133
Chi . square = 5.133
critical value of chi square a t degrees of freedom (n1-1) * (n2-1) = 1* 1 = 1
at 0.95% level = 3.841
calculated Chi square > critical Chi square
HENCE REJECT NULL HYPOTHESIS
Men Women More true of men 0.6 0.52 more true of women 0.4 0.48 observed Men Women More true of men 216 228.8 444.8 more true of women 144 211.2 355.2 360 440 800 expected Men Women More true of men 200.16 244.64 more true of women 159.84 195.36