POLS3001 University of Utah Week 9 Inferential Statistics Problems Paper
Question Description
Exercise 1
In the 2012 CCES (Cooperative Congressional Election Study), individuals were asked what percent of a budget deficit should be made up of spending cuts (0-100%). For those with children under 18, the mean value was 59.44% with a standard deviation of 25.763%. For those without children, the mean value was 58.04% with a standard deviation of 25.80%. The weighted sample sizes were 10093 and 30492, respectively. Using a t-test, can we confidently reject the possibility that, in the population from which the sample was drawn, that the true difference is 0%, i.e., the means for each group are the same? Why or why not?
Exercise 2
Refer back to #1. This time, we are only sampling individuals from the state of Utah. The means for each group are 64% and 60.55%, respectively. The standard deviations are 20.939 and 23.825, and the weighted sample sizes are 169 and 264. Using a t-test, can we confidently reject the possibility that, in the population from which the sample was drawn, that the true difference is 0%, i.e., the means for each group are the same? Why or why not?
Exercise 3
Using this data, use STATA to calculate an inferential statistic to determine if group 2 differs from group 1.
Exercise 4
A random sample of 1022 Italians age 15 and above is taken as part of a 2008 Eurobarometer. 51% percent state that their country has benefited from their country’s membership in the European Union (49% do not). Using a 95% confidence interval test, can we confidently reject the possibility that the true percentage who feel benefited in the population is 50%? What about 60%?
Exercise 5
The following table gives the breakdown, by gender, of feelings toward immigration for a random sample of residents of Spain.
Male
Female
Total
Beneficial
324
334
658
Don’t Know
59
76
135
Not Beneficial
124
116
240
Total
507
526
1033
Answer the following questions:
Using percentage differences in this sample, which gender group was more likely to consider immigration to be beneficial? By what percentage point difference?
Using chi-square, can we confidently claim that men and women differ on immigration in the population rom which this sample was randomly drawn? Be precise in your answer.
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