##### Reference no: EM13528928

**Question 1: **Each of the following proportions is based on survey responses. For each proportion, use the ±2 rule of thumb to determine the 95 percent confidence interval.

A. When asked if they are satisfied with their financial situation, .29 said "very satisfied" (n = 121).

B. When asked if people can be trusted, .32 said "yes" (n = 100).

C. Of the individuals in a survey, .40 still live in the same city they lived in when they were 16 years of age (n = 225)

**Question 2: .** Scholars of political development have investigated the so-called oil curse, the idea that oil-rich countries tend not to develop democratic systems of governance) that "oil and democracy do not mix."17 Framing this idea in the form of a hypothesis: In a comparison of countries, those having economies less dependent on oil wealth will be more democratic than will countries having economies more dependent on oil wealth. Consider the following data, which present information for twenty countries with non-oil-dependent economies and fifteen countries with oil-dependent economies. The dependent variable is a 7-point level-of-democracy scale, with higher scores denoting more democracy. Here are the mean values and standard errors of the democracy scale for nonoil-dependent and oil-dependent countries:

Oil-dependent economy? Mean democracy scale Standard error

No 4.7 .51

YES 2.6 .28

A. State the null hypothesis for the non-oil-dependent/oil-dependent comparison.

B. Calculate the difference between the means of the democracy scale for non-oil-dependent and oil-dependent countries, Calculate the standard error of the difference. Calculate the t-statistie.

C. Does the mean difference pass the 1.645 test of significance? Explain how you know.

D. Based on these results, suppose a researcher decides to reject the null- hypothesis. Is this decision supported by the statistical evidence? Explain.

**Questions 3:** Below are two conventional wisdoms, statements generally believed' to be accurate descriptions of the world. Accompanying each statement are data (from the 2008 General Social Survey) that allow. you to test each conventional wisdom, For each statement:

A. State the null hypothesis.

B. Calculate the difference between the proportions or means.

C. Calculate the standard' error of the difference in proportions or means.

D. Using the eyeball test, (I) state whether you would accept the null hypothesis or reject the null hypothesis and (ii) explain your reasoning. Conventional Wisdom ONE: Hispanics have larger families than non-Hispanics. The 2008

General Social Survey asked respondents how many children they have. Hispanic respondents had an average of 1.98 children (standard error =, 12), whereas non-Hispanics averaged 1.93 children (standard error = .04).

CONVENTIONAL 'WISDOM Two: Southerners are more likely than no southerners to own a gun.

According to the 2008 General Social Survey, .43 of southern respondents owned a gun (n =482), compared with .33 of nonsoutherners (n = 855).

**Question 4:** On December 18,2010, the U.S. Senate voted on the question of whether to repeal the don't ask don 't tell Policy (DADT) Regarding gays in the military. The relationship between party affiliation and vote IS shown-in the following table

Party

Repeal DADT? Democrat Republican Total

No 0 31 31

Yes 55 8 63

Total 55 39 94

(Note: Two independents also voted yes. Four senators, one Democrat and three Republicans, did not vote.)

A. Calculate chi-square for this table. Show your work. Draw a table just like the one above, leaving room in each cell to record these numbers: observed frequency f_{o}), expected frequency f_{e}),

F_{o }-f_{e}(f_{0}-f_{e})^{2} and (f_{0}-f_{e})^{2}/f_{e}

B. Use chi-square to test the null hypothesis that, in the population from which the sample was drawn, there is no relationship between party and vote. Using Table 7-7) find the appropriate critical value (use the .05 level of significance). (i) Write down the critical value. (Ii) Should you reject the null hypothesis or not reject the null hypothesis? (iii) Explain your reasoning.

C. Calculate lambda for this table. (i) Show your work. (il) Write a sentence explaining exactly what the value of lambda means. (iii) State whether the relationship is weak, moderate, moderately strong, or strong.

**Question 5:** The following table of raw frequencies can be 'used to test this hypothesis: In a comparison of individuals, people with lower levels of education will express stronger support for the death penalty than will people with higher levels of education.

Support for death penalty

Education High school or less some college College or higher

Not Strong 47 43 56

Strong 49 50 35

A. Consider the way the table is arranged. If the hypothesis is correct, should we find a positive sign on Somers' d_{yx} or a negative Signon Somers' d_{yx}? Explain how you know.

B. Calculate Somers' d_{yx} for this table. Show your work. On a sheet of paper, label three columns: Concordant pairs (C), Discordant pairs (D), and Tied pairs (Ty-Work your way through the table, recording and computing each concordant pair, discordant pair, and tied pair.

C. Examine the value of Somers' dyx that you calculated in B. Exactly what does this value tell you about your ability to predict death-penalty opinions using education as a predictive instrument?

D.State whether the relationship is weak, moderate, moderately strong, or strong.