This final examination will cover the entire semester.  There will be multiple choice and statistical questions.  Please bring a calculator and a pencil with an eraser.  Do NOT bring the Guide to Computing Descriptive Statistics or the Guide to Computing Margins of Error.  Fresh copies of these will be included with the exam.

Multiple Choice Questions.  The best way to review for the multiple choice questions is to study the Review Glossary at the end of each chapter.  You may also find it useful to read over the lecture notes.  It is also a good idea to review the questions on the first two examinations, which have been returned to you.

Statistical Questions. These questions, also, will be similar to those on the first two exams.  If you did not get these questions on the first two examinations, make sure you learn how to solve them for the final.  The best way to do this is to work some problems, such as those on this review page.  The answers will be posted, but it is best to consult them after you have worked the problems yourself.

Percentage Questions.
Consider the following data:

45 men support Schundler    25 women support Schundler
35 men support McGreevy     80 women support McGreevy

To answer these questions, you should first put the data in a table and compute the row and column totals.

                   Men            Women    Total

       Schundler   45             25       70

       McGreevy    35             80       115

       Total       80             105      185
 
 

1.    What percentage of the men support Schundler?  The number of men supporting Schundler is 45, the total number of men is 80, so the answer is 45/80 *100 or 56.3%.  Always give three significant digits
2.    What percentage of the Schundler supporters are men?  This one is the number of men supporting Schundler divided by the number of Schundler supporters  45/70 * 100 or 64.3%
3.    What percentage of the women support McGreevy?  76.2%
4.    What percentage of the McGreevy supporters are women?  69.6%

Expected Frequency Questions.
5.    If there were no relationship between gender and candidate preference, how many man would we expect to support Schundler?  Note: this questions asks for a frequency [the "expected frequency"], not for a percent.  The easiest way to compute an expected frequency is to multiply the row total for the cell in question by the column total for that cell and divide by the grand total.  In this case, the rot total is 70, the column total 80 and the grand total 185.  Answer 30.3.  If you make this a percent, 30.3%, it is wrong, since this is a frequency, not a percent.
6.    If there were no relationship between gender and candidate preference, how many women would we expect to support Schundler?  39.7

To do expected frequencies, you start with the same table.   There are three ways to do them, one is shown in red, another - the easiest, in blue.
                   Men            Women    Total

       Schundler   45 .378*80=30.24 25       70   .378 (this is the "row proportion")
One way to get the expected frequencies is to compute the row proportions and multiply them by the column totals.  Or you could compute the column proportions and mutiply them by the row totals.
       McGreevy    35 .622*80      80      115   .622

       Total       80             105      185   -

The easiest way to get expected frequencies is to multiply the row total associated with the cellin question with the column total associated with that cell and divide by the grand total.  For example, for the cell giving frequencies for the men voting for Schundler the expected frequency would be (70 * 80)/185 = 30.27 the grand total, 185, is the sum of both the row and the column totals.  Note that the result is slightly different because .378 is rounded off.  The two methods are arithmetically equivalent, the second involves less rounding and less risk of error.
 

Descriptive Statistics Questions.  These are explained in the Guide to Computing Descriptive Statistics.
7.   Five students make the following scores on this test: 85, 65, 92, 78, 51
8.   What is the mean score?  The sum of the scores is 371, N is 5, so the mean is 74.2.
9.   What is the median score?  The median is the one in the middle, but only after you arrange the scores in numerical order:  51, 65, 78, 85, 92.  The median is 78.
10.  What is the standard deviation of the scores?  To compute the standard deviation, follow the instruction in the Guide to Computing Descriptive Statistics.  Answer:  16.4

Here are the computations for the standard deviation, following the Guide to Computing Descriptive Statistics.
 
 

X = Each Score	The Mean	X - the Mean	X-the mean squared
85	74.2	10.8	116.64
65	74.2	-9.2	84.64
92	74.2	17.8	316.84
78	74.2	3.8	14.11
51	74.2	-23.2	538.24

7.  Now add up the fourth column, this is the Sum of Squares.  Write it here:  . 1070.78 .

8.  Divide the sum of squares by the number of cases, minus one (N-1)  N = 5 since their are five cases, no N-1=4, 1070.78/4 = 267.7.  This is the variance.  Write it here: .   267.7  .

9.  The standard deviation is the square root of the variance.  Write it here: .   16.4  .

Sampling Questions.  Follow the instructions in the Guide to Computing Margins of Error.
11. In a college class with 125 students, 48 of whom are male, the mean on the final exam was 79. The standard deviation was 7. What is the margin of error for this mean? This is a mean score question, so we use Formula 4.  2 * 7/sqrt(125) = 1.25
12. What would the lower bound of the 95% confidence interval be for this mean?  Subtract the Margin of Error from the Mean, 79 - 1.25 = 77.8.  Note, this is not 77.8% unless you assume the test scores are percentage scores.
13. A researcher wants to obtain a margin of error of no more than 10% in a survey of a county with a population of 30,000. How large a sample is needed?  This is a sample size question, so we use Formula Three, 1/(.10*.10)= 100
14. 60% of the Republican respondents in a survey of a state with seven million Republican voters voted for Bush, 40% for Gore. There were 1625 respondents, of whom 1000 were Democrats, 600 Republicans and 25 other. What is the margin of error for the percent voting for percent of Republicans voting for Bush?  This question asks about the Republicans, so N = 600.  We are given a percent, 60%, so we use Formula Two.  Answer 4.0%
15. A survey is to be conducted of attitudes among white and nonwhite respondents in Camden County. The population is 300,000. Of this population, 80% is white, 20% nonwhite. The researcher wants to achieve a 6% margin of error for the estimates for each of the groups. How large a sample is needed?  A 6% margin of error requires 278 people, we need 278 from each of two groups, so the answer is 556.
16. In a survey of community residents, the mean income was $38,745 with a standard deviation of $1,345. There are 370,000 residents in the community. 100 were sampled in the survey. What is the margin of error for this mean score?  $269
17. What would the lower bound of the confidence interval be for this mean?   $38,745 - $269 = $38,476.
18. What would the upper bound of the confidence interval be?  $38,745 + $269 = $39,014.
19. A survey of the South Jersey respondent had 200 male respondents and 275 female respondents.  110 men and 250 women voted for Gore.  What is the margin of error for the percentage voting for Gore in this survey?  For this one, you have to compute the percents yourself!  There are 475 respondents and 360 voted for Gore, so 75.8% voted for Gore.  We use Formula Two with N = 475 and p = .758  = 3.93%
20. What is the margin of error for the percentage of women voting for Gore?  Here N is 275 and p = .909 = 3,47%

Regression questions.
The following variables were used in a regression analysis:
AUTO THEFT - MOTOR VEHICLE THEFTS PER 100,000
POV LINE - PERCENTAGE OF POPULATION BELOW THE POVERTY LEVEL
DENSITY - POPULATION PER SQUARE MILE
The results were as follows:

Analysis of Variance
Dependent Variable: AUTO THEFT
N: 50          Missing: 0
Multiple R-Square = 0.070     Y-Intercept = 250.561
Standard error of the estimate = 188.588
LISTWISE deletion (1-tailed test)     Significance Levels: **=.01, *=.05
 Source Sum of Squares DF Mean Square F Prob.
 REGRESSION 125249.515 2 62624.757 1.761 0.183
 RESIDUAL 1.672e+06 47 35565.585
 TOTAL 1.797e+06 49
         Unstand.b Stand.Beta Std.Err.b t
POV LINE 11.349     0.195     8.382     1.354
DENSITY   0.179     0.224     0.115     1.555

21.  What are the independent variables in this last analysis?  POV LINE and DENSITY

22.  What is the dependent variable in this analysis? AUTO THEFT

23.  Which variable is the best predictor of the dependent variable?  The best predictor is the independent variable with the highest Standardized Bets.  DENSITY is highest with a Stand.Beta of .224

24.  What percentage of the variance in the dependent variable is explained in this analysis?  This is the Multiple R-Square converted to a percentage, 7.0%

25. Fill in the blanks in this formula:  Here we fill in the intercept and the undstandardized betas AUTO THEFT = 250.561 +   ( 11.349 * POV LINE) + ( 0.179   * DENSITY)

26. What would the predicted rate of auto theft be for a state with 15% of its population below the poverty line and 200 people per square mile?   Here we use the formula in the preceeding question, substituting the values for the independent variables.  We leave them in the original unit of measurement that was used to compute the equation, % below the poverty line and number of people per square mile.  AUTO THEFT = 250.561 +   ( 11.349 * 15 ) + ( 0.179   * 200 ) = 456.60.
27. What would the predicted rate of auto theft be for a state with 10% of its population below the poverty line and 200 people per square mile?  399.85
28. What would the predicted rate of auto theft be for a state with 5% of its population below the poverty line and 100 people per square mile?  325.2
29. What would the predicted rate of auto theft be for a state with 9% of its population below the poverty line and 180 people per square mile?  384.92
30.  On average, how much does the auto theft rate go up for each one percent increase in the poverty rate?  11.349
31.  On average, how much does the auto theft rate go up for each 10 additional people per square mile? 1.79 (the regression coefficient is .179, but this is for one unit of DENSITY.  The questions asks for 10, so we multiply it by 10.