Statistic work
mehett
statistic_work_.pdf
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4. A researcher is interested in the level of ideological consistency among Democrats and Republicans.
She creates a measure of ideological consistency that ranges from 0 (total lack of consistency) to 10
(absolute consistency). What kind of statistical test should the researcher employ?
A. Chi-Square
B. Guessing
C. Differences of Means Test
D. Correlation
5. Regression in appropriate when our dependent variable is measured at what level of measurement?
A. Interval
B. Ordinal
C. Nominal
D. Dummy
6. A type one error occurs…
A. When we incorrectly fail to reject the null hypothesis even though it is false
B. When we have measurement error in one of our variables
C. When we incorrectly reject the null hypothesis even though it is true
D. When the results of our analysis do not support our alternative hypothesis
7. Below are four different hypotheses, which of the four should be tested using a one tailed test?
A. Democrats and Republicans will differ in their support for tax cuts
B. Republicans will be more supportive of tax cuts than Democrats
C. Republicans and Democrats will not differ in their support for tax cuts
D. Support for tax cuts will differ by party
8. In Chi Square testing our expected frequencies are…
A. The frequencies we would expect to observe if the null hypothesis was true
B. The frequencies we actually observe
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C. The frequencies we would expect to observe if the alternative hypothesis was true
D. The frequencies we would expect to observe if the null hypothesis was false
9. A researcher is interested in testing whether males and females differ in their level of political
knowledge. To test this the researcher administers a political knowledge test to a sample of 10 males
and 10 females. Tests are scored out of 100 points. What statistical test should the researcher use to
test her hypothesis that males and females will differ in their level of political knowledge. (Hint think
about what test is appropriate for the level of measurement of these variables)
A. Correlation
B. Chi Square
C. Difference of Means Test
D. Standard Deviation
10. Outliers are a particular problem for which statistical test?
A. Correlation
B. Regression
C. Difference of Means
D. Chi Square
11. In regression our constant (Y intercept) is equal to:
A. The predicted value of Y when all of the X’s in our model = 0
B. The expected change in Y associated with a one unit change in X
C. The predicted value of X when all the Y’s in our model = 0
D. The expected change in X associated with a one unit change in Y
12. If we decrease our probability of making a Type 1 error we…
A. Decease our probability of making a Type 2 error
B. Increase our probability of making a Type 2 error
C. Have the same probability of making a Type 2 error
D. Have 0 probability of making a Type 2 error
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13. Correlation and regression analysis are appropriate for which type of relationship?
A. A curvilinear relationship
B. An exponential relationship
C. A linear relationship
D. A non-linear relationship
14. When we are testing for a difference in means and we fail to reject the null hypothesis this indicates
that…
A. The means of the two samples are exactly identical
B. The means of the two samples are significantly different
C. Any difference between the means of the two samples is most likely a result of true population
differences
D. Any difference between the means of the two samples is most likely a result of sampling error
15. If there is no relationship between two variables there correlation would be equal to…
A. -1
B. 0
C. .5
D. 1
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Part 2 Computational Questions: Write in the correct answer (70 points)
16. A researcher theorizes that Democrats and Republicans will differ in their support for gun control.
He surveys 25 Democrats and 15 Republicans about their support for gun control legislation and records
their answers on a standardized measure where higher scores represent greater support for gun control.
He finds that the mean level of support among Democrats is 6.0, with a standard deviation (S) of 1.2.
The mean level of support for Republicans is 4.9, with a standard deviation (S) of 1.4. (8 points)
A. Using a difference of means test, test the null hypothesis that there is no difference between
Democrats and Republicans in their support for gun control legislation.
B. Do the results of this test support the researcher’s hypothesis?
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17. A researcher is interested in determining whether reading an article against the death penalty
makes people less supportive of the death penalty. To test this hypothesis, she conducts an experiment
where she gives 5 participants an article to read that is critical of the death penalty. 5 other participants
do not get to read the article. The researchers then asks all 10 participants how supportive they are of
the death penalty to see whether there are any differences in support for the death penalty between
the two groups. She records their answers on a 10 point scale with higher scores indicating more
support for the death penalty. Her results are reported in the table below. (10 points)
A. Using these results and a difference of means test, test the null hypothesis that participants will be
equally supportive of the death penalty after reading the article.
Did not read article
Read article
2 1
5 5
6 6
7 4
7 4
B. Do the results of this test support the researcher’s hypothesis?
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18. A researcher is interesting in determining whether favorite ice cream flavors are equally distributed
among the population. He asks 20 randomly selected people to report their favorite ice cream flavor.
The results are reported below. (8 points)
A. Using a Chi Square test, test the null hypothesis that favorite ice cream flavors are equally distributed
among the population
Ice Cream
Flavor
Observed
Frequency
Chocolate 11
Vanilla 6
Strawberry 3
Pistachio 0
Total 20
B. What can you conclude about the distribution of favorite ice cream flavors in the population?
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19. Below are the results from a cross tabulation of gender and political ideology. (8 points)
Liberal Moderate Conservative Total
Male 30 25 50 105
Female 40 35 20 95
Total 70 60 70 200
A. Fill in the table below with the expected frequency for each cell.
Liberal Moderate Conservative
Male
Female
B. Calculate the Chi Square test statistic
Cell Observed
Frequency
Male Lib. 30
Male Mod. 25
Male Cons. 50
Female Lib. 40
Female Mod. 35
Female Cons. 20
Total 200
C. Using your Chi Square statistics from part B, test the null hypothesis that there is no difference in
political ideology by gender.
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D. Based on the results of this test what can you conclude about the relationship between gender and
ideology?
20. A researcher theorizes that people who read more books will do better on a vocabulary quiz. To this
hypothesis the researcher surveyed 4 people and asked them the number of books they had read in the
past year. He also gave them a short vocabulary quiz, which was scored out of 10 points. The results are
reported below. (6 points)
A. Calculate the correlation between number of books read and scores on the vocabulary quiz.
# of Books Read Quiz Score
5 8
4 6
6 9
1 5
B. What does the correlation say about the size and strength of the relationship between the number of
books read and vocabulary quiz scores?
C. Is the correlation significant? Why or not?
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21. Below is a correlation matrix between X, Y, and Z. (4 points)
A. Find the partial correlation between X and Y controlling for Z
22. Use the table below to regress X on Y (10 points)
X Y
5 6
9 7
6 5
8 6
2 2
A. Find the slope coefficient (b) for X and explain what it means.
B. Find the constant (a) and explain what it means.
X Y Z
X 1.00 .77 .96
Y .77 1.00 .73
Z .96 .73 1.00
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C. Find 𝑟2 for the regression and explain what it means.
D. Write the regression equation and plot the line on the scatterplot below.
E. What is the predicted value of Y when X = 4?
0
1
2
3
4
5
6
7
0 1 2 3 4 5 6 7 8 9 10
Y
X
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23. A researcher theorizes that the more educated a state is the higher voter turnout in the state will be.
To test this theory the researcher measures the percentage of the population in each state that has a
college degree and also the state’s voter turnout in the last election. The researcher then regresses the
percent of the state with a college degree on the state’s voter turnout. The results from the regression
are reported below (8 points)
A. What is the constant and how should it be interpreted in the terms of this example.
B. What is the slope coefficient for the college variable and how should it be interpreted in terms of this
example?
C. Is the slope coefficient on the college variable significant? Why or why not?
D. Do the results of this regression support the researcher’s hypothesis? Why or why not?
_cons 47.74297 5.649103 8.45 0.000 36.38469 59.10125
college .4498426 .2153555 2.09 0.042 .0168413 .8828438
turnout Coef. Std. Err. t P>|t| [95% Conf. Interval]
