POLITICAL SCIENCE 551

Problem Set 12

  1. One survey reported the mean weight of 17 year old females in the U.S. to be 118 pounds, with a standard deviation of 11 pounds. If the sample size is 484, what is the 95% confidence interval of weight of all 17-year old females in the United States?


  2. In the Political Science Department, 20% of the persons who take a Ph.D. exam fail the exam on the first try. In a recent exam period, three out of five persons who took a Ph.D. exam in International Relations for the first time, failed the exam. If you were one of the persons who failed, could you make a "statistical argument" that there was something wrong with the exam? What would the argument look like? How might someone counter the argument?


  3. The mean height (µ) of adult males in the United States is 68.5 inches and the standard deviation (sigma) is 2.5 inches. Over the last three presidential elections, 25 men have run for the office; their average height is 70 inches. Are presidential candidates taller than average?


  4. You do a survey of undergraduates at the university in which you ask a series of questions to measure the degree of interest in the presidential campaign. When you compare upperclasspersons and underclasspersons, you find the following: 
    5.              upper                   under
              n=25                   n=25 
            mean=7.65              mean=6.00
           variance=6.50         variance=5.90
    where the means are the mean interest scores. What is the 99% interval estimate for the difference in the means? Could you conclude that the population mean for underclasspersons is different than that for upperclasspersons?

  5. Given the null hypothesis that the proportion of men who oppose abortion on demand is the same as the proportion of women, and that that proportion is .3 (i.e., 30% of both men and women oppose abortion on demand), what is the likelihood of rejecting the null hypothesis (i.e., the power of the test) at the .05 level using a sample size of 50 men and 50 women if the true difference in the proportion is .01? .05? .10? .25?

    6. THE REMAINING QUESTIONS USE THE DATA SHOWN ON THE NEXT PAGE. THESE DATA ARE IN EITHER STATA OR EXCEL FORMAT.

  6. Is there a relationship between region and liberalism?

  7. Is there a relationship between party and seniority (i.e., is the average seniority level of Republican representatives different from the average seniority level of Democratic representatives)? (Note: seniority does not have a normal distribution since it has a uniform distribution between 1 and 435. However, the variance (sigma2) of a uniform distribution is equal to the following: 
    8.                                   (maximum - minimum)2
                variance  =   ---------------------------------
                                            12
    where "maximum" and "minimum" refer to the population not the sample.)

  8. Describe the relationship between percent Democratic (in the 1986 election) and liberalism in voting (as measured by the ADA score); how strong is the relationship? Is it significant?

  9. Obtain both a point estimate and an interval estimate of the mean liberalism score for all Representatives. 

Partya    % Democratic    ADA Liberalismb   Seniority  Committeec   Regiond
          Vote in 1986     Score 1987-88      Rank      Position 

  1            53.4             68            386          3            1
  1            61.2             75             53          1            3 
  1            85.1             36             10          1            2
  2            43.7             10            112          2            3
  2            48.3             21            299          2            3
  1            56.8             94            325          3            1
  2            38.2              0            381          3            1
  2            47.2             21            174          2            3
  1            51.2             83            201          2            1
  1            57.8             28             86          1            2
  1            49.1              5            301          3            2
  2            46.1             31            236          2            3
  2            41.2             10             27          1            1
  1            61.8             89            223          2            3
  1            50.3             56            377          3            1
  2            46.1             13            121          2            3
  1            58.3             58            173          2            1
  2            43.1             41             47          1            3
  1            58.5             23             15          1            2
  1            60.3             95            313          3            1
  1            57.2             85            222          2            3
  2            48.1             15            189          2            3
  2            38.3              8            205          1            2
  2            41.7              4            305          2            1
  2            45.1             29            293          1            3
  1            55.6             85            270          2            1
  1            69.3             45            300          2            2
  1            52.6             78            124          3            1


aThe code value 1 stands for Democrat and 2 for Republican.


bYou may assume this to be an interval score.


cThe code value 1 stands for "good", 2 for "fair", and 3 for "poor".


dThe code value 1 stands for North, 2 for South, and 3 for West.