1. (Dataset: gss. Variables: egalit_scale, wtss.) The 2012 General Social Survey asked people a series of questions designed to measure how egalitarian they are—that is, the extent to which they think economic opportunities and rewards should be distributed more equally in society. The gss variable egalit_scale ranges from 1 (low egalitarianism) to 35 (high egalitarianism). The 2012 GSS, of course, is a random sample of U.S. adults. In this exercise, you will analyze egalit_scale using wtd.t.test and CI95. You will then draw inferences about the population mean.
1. Run wtd.t.test on gss$egalit_scale, with the test value set to 0. (Be sure to weight by gss$wtss.) Egalitarianism has a sample mean of (Fill in the blank.) _________________.
Based on the results you obtained in part A, run CI95. There is a probability of .95 that the true population mean falls between an egalitarianism score of (Fill in the blank.) _______________ at the low end and a score of (Fill in the blank.) _______________ at the high end.
A student researcher hypothesizes that social work majors will score significantly higher on the egalitarianism scale than the typical adult. The student researcher also hypothesizes that business majors will score significantly lower on the egalitarianism scale than the average adult. After administering the scale to a number of social work majors and a group of business majors, the researcher obtains these results: Social work majors’ mean, 20.1; business majors’ mean, 18.8. Run wtd.t.test, specifying a test value of 20.1. Using the mean difference (“Difference”) and standard error, run CI95. Run wtd.t.test again, specifying a test value of 18.8. Run CI95, using the mean difference and standard error.
Based on your analyses, and applying the .05 test of significance, you can infer that (Check one.)
❑ Social work majors probably are not more egalitarian than most adults.
❑ Social work majors probably are more egalitarian than most adults.
Explain your answer.
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Based on your analyses, and applying the .05 test of significance, you can infer that (Check one.)
❑ Business majors probably are not less egalitarian than most adults.
❑ Business majors probably are less egalitarian than most adults.
Explain your answer.
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5. Refer to the P-value you obtained from your analysis of
the business majors’ mean. (Fill in the blanks.)
If in the population there is no difference between the mean of egalit_scale and the business majors’
mean, the observed difference of _______________
would occur _______________ of the time by chance. 2. (Dataset: gssD. Variables: age2, int_info_scale.) Are older
people interested in a wider variety of social, economic, political, and scientific issues than are younger people? Or do younger people and older people not differ significantly in the scope of their interests? The gssD dataset contains int_info_scale, which measures respondents’ level of interest in 10 different issue areas. Scores range from 0 to 20, with higher scores denoting higher levels of interest. The gssD also has age2, which takes on two values: "<=30" for="" respondents="" 30="" years="" old="" or="" younger="" and="" “="">=31” for respondents older than 30. Run wtd.ttestC, using int_info_scale as the dependent variable and age2 as the independent variable.
1. Fill in the table below.
According to the null hypothesis, in the population from which the sample was drawn, the difference between the mean for people older than 30 and the mean for people 30 or younger is equal to (Fill in the blank.) _______________.
In this analysis, the upper 95% CI includes 0. This fact alone tells you that the P-value (Check one.)
❑ must be greater than .05. ❑ must be greater than .025. ❑ must be 0.
4. Using the .05 level of statistical significance, you can infer that (Check one.)
❑ The older age group and the younger age group do not differ significantly in their level of interest in current issues.
❑ The older age group scores significantly higher on the level of interest scale than does the younger age group.
❑ The older age group scores significantly lower on the level of interest scale than does the younger age group.
5. Your inferential decision, therefore, is (Check one.) ❑ accept the null hypothesis.
❑ reject the null hypothesis.
3. (Dataset: gssD. Variables: sibs, relig2, authoritarianism, sex.) Here are two bits of conventional wisdom, beliefs that are widely accepted as accurate descriptions of the world. Conventional Wisdom 1: Catholics have bigger families than do Protestants. (Dependent variable: sibs, number of siblings; independent variable: relig2, "Protestant"/ "Catholic".) Conventional Wisdom 2: Men have stronger authoritarian tendencies than do women. (Dependent variable: authoritarianism, ranging from 0 [low authoritarianism] to 7 [high authoritarianism]; independent variable: sex.)
1. In this exercise, you will use wtd.ttestC to test these ideas and see how well they stand up to the statistical evidence. Run the analyses. Record the results in the following table.
Consider the following statement: “According to the statistical evidence, we can reject the null hypothesis for Conventional Wisdom 1.” Is this statement correct or incorrect? (Circle one.)
Incorrect Correct
Explain your answer, making specific reference to the statistics in part A.
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Consider the following statement: “The statistical
evidence supports Conventional Wisdom 2.” Is this statement correct or incorrect? (Circle one.)
Incorrect Correct
Explain your answer, making specific reference to the statistics in part A.
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4. (Dataset: gss. Variables: partyid_3, sex, wtss.) In one of this
chapter’s guided examples, you analyzed the nes dataset and found a statistically significant difference between the
proportions of males and females who are Democrats. The gss dataset also contains a measure of party identification, partyid_3 ("Dem" / "Ind" / "Rep"). However, the General Social Survey uses a different sampling frame (all U.S. adults vs. voting-eligible citizens) and somewhat different question wording for its party identification question. Will the gss dataset also reveal a statistically significant difference in the proportions of males and females who are Democrats?
1. Create a numeric indicator, named gss$dem, for the “Dem” category of gss$partyid_3. Run prop.testC. Record the results in the following table:
2. Does the statistical evidence support the hypothesis that men are less likely than women to be Democrats? Answer yes or no and explain, making explicit reference to the evidence in part A.
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