Deck 8: Using Sample Slopes to Talk About Populations: Inference and Regression

Question 1

In a sampling distribution of sample slopes, what is each "building block" in the distribution?

A) the difference between a sample slope and the population slope
B) a sample mean
C) a predicted value using the regression equation
D) a sample slope

Answer 1

D

Question 2

In inference with regression, what does the p-value represent?

A) the probability that the population slope is zero
B) the probability that the population slope is not zero
C) the probability that the population slope is equal to the sample slope
D) the probability that the sample slope is real

Answer 2

A

Question 3

Which of the following is not needed to calculate the estimate of standard error?

A) the standard deviation of the independent variable
B) the r-squared value
C) the sample slope
D) the sample size

Answer 3

C

Question 4

Everything else remaining constant, the larger the sample size:

A) the smaller the standard error
B) the smaller the t-value
C) the smaller value for r-squared
D) the smaller the slope

Question 5

Using a sample of 2,000, a researcher calculates a standard error of the slope, and finds it to be 2. What would the slope have to be to achieve statistical significance?

A) 1
B) 2
C) 3
D) 4

Question 6

We use GSS2008 data to see if age affects the number of times one visited an art museum in the past year. We find, with a sample size of 1496, that both the slope and the value of the standard error are .009. From this, what can you conclude?

A) The slope is significant at the p<.001 level
B) The slope is significant at the p<.01 level
C) The slope is significant at the p<.05 level
D) The slope is not statistically significant.

Question 7

We use GSS2008 data to see if age affects number of times one visited a zoo in the past year. We find, with a sample size of 1496, that the value of the slope is -.019 and the value of the standard error is .004. From this, what can you conclude?

A) The slope is significant at the p<.001 level
B) The slope is significant at the p<.01 level
C) The slope is significant at the p<.05 level
D) The slope is not statistically significant.

Question 8

We use GSS2008 data to see if age affects number of times one visited a public library in the past year. We find, with a sample size of 1489, that the value of the slope is -.072 and the value of the standard error is .038. From this, what can you conclude?

A) The slope is significant at the p<.001 level
B) The slope is significant at the p<.01 level
C) The slope is significant at the p<.05 level
D) The slope is not statistically significant.

Question 9

We observe the same slope for a sample of men and a sample of women, and for both slopes, p<.05. If we combined the samples and found a combined slope, which of the following must be false:

A) the significance of the combined slope is p<.001
B) the significance of the combined slope is p<.01
C) the significance of the combined slope is p<.05
D) the significance of the combined slope is p>.05

Question 10

With regard to statistical significance, the textbook repeatedly stresses the important role of:

A) variation in the dependent variable
B) variation in the independent variable
C) explained variation
D) sample size

Question 11

What symbol is most typically used to represent the statistical significance of a slope?

A) $
B) #
C) *
D) !

Question 12

Most regression results related to statistical significance are reported as:

A) zero-tailed
B) one-tailed
C) two-tailed
D) three-tailed

Question 13

The BMI and income example in the textbook found:

A) a statistically significant effect for both men and women
B) a statistically significant effect for men, but not for women
C) a statistically significant effect for women, but not for men
D) neither men nor women had a statistically significant effect

Question 14

In the example regarding age and attitudes toward immigration, those born outside the U.S. had a _______ slope than those born in the U.S., but this slope was ____________.

A) smaller, not statistically significant
B) smaller, statistically significant
C) larger, not statistically significant
D) larger, statistically significant

Question 15

Which national dataset does Ansell use in his research on support for social security spending?

A) the General Social Survey
B) the American National Election Studies
C) the Panel Study of Income Dynamics
D) the World Values Survey

Question 16

In Ansell's article about support for social security spending, his key independent variable is:

A) how much a respondent's house had appreciated
B) respondent's family income
C) respondent's age
D) the respondent's tax rate

Question 17

Ansell's measure of support for social security is unique in that:

A) it uses five different survey questions to gauge support
B) it defines social security quite broadly
C) it measures changes in support over two time periods
D) it tests respondent's understanding of the Social Security program

Question 18

According to the textbook, one of the most impressive aspects of Ansell's article on support for social security is:

A) )Ansell's carefully selected random sample
B) Ansell's calculation of statistical significance in multiple ways
C) Ansell's use of a single data source to produce his results
D) Ansell's careful description of the actual effect sizes

Question 19

What dataset does Downey use in his study of family size and grades?

A) The National Educational Longitudinal Study
B) The National Longitudinal Survey of Youth
C) The National Survey of Families and Households
D) The National Longitudinal Survey of Adolescent Health

Question 20

How many cases were in Downey's regression of family size on grades?

A) only 250
B) only 500
C) nearly 1,000
D) nearly 17,000

Question 21

Which of the following best characterizes the findings of Downey's study of the effect of family size on grades?

A) Children from large families get slightly better grades than children from smaller families.
B) Children from smaller families get slightly better grades than children from larger families.
C) Children from smaller families get much better grades than children from larger families.
D) Children from smaller families and children from larger families get the same grades.

Question 22

In a typical SPSS regression, how many boxes of output are involved?

A) 2
B) 4
C) 6
D) 8

Question 23

For which the following scenarios is the Adjusted r-squared most likely to differ from the regular r-squared?

A) When the sample size is small and the number of independent variables is large
B) When the sample size is large and the number of independent variables is large
C) When the sample size is small and the number of independent variables is small
D) When the sample size is large and the number of independent variables is small

Question 24

In SPSS regression output, Sum of Squares Regression is the equivalent to:

A) the total amount of explained variation
B) the total amount of unexplained variation
C) the total amount of variation
D) the total amount of residual variation

Question 25

In SPSS regression output, Sum of Squares Residual is the equivalent to:

A) the total amount of explained variation
B) the total amount of unexplained variation
C) the total amount of variation
D) the total amount of residual variation

Question 26

Someone collects data from your statistics class, runs a regression, and then presents the results, claiming that there is a statistical significant relationship between the percentage of classes you attend and your grade point average. Critique this person's finding.

Question 27

Use the following GSS2008 results to explain how a slope could be statistically significant, yet substantively insignificant:
TVHOURS = 1.86 + .02 (AGE); Significance of slope: p<.001

Question 28

Here are data from the 16 American Indians in the GSS2008:
Independent Variable: Respondent's Father's Years of Education
Dependent Variable: Respondent's Years of Education
Standard Deviation of Independent Variable: 3.18
Standard Deviation of Dependent Variable: 2.50
Value of slope: .33
Value of r-squared: .18
Sample size: 16
Can we confidently claim that there is a relationship in the population of American Indians?

Question 29

Here are data from the 39 Hispanic women in the GSS2008:
Independent Variable: Woman's Number of Siblings
Dependent Variable: Women's Number of Children
Standard Deviation of Independent Variable: 3.24
Standard Deviation of Dependent Variable: 1.38
Value of slope: .16
Value of r-squared: .14
Sample size: 39
Can we confidently claim that there is a relationship in the population of Hispanic women between number of siblings and number of children?

Question 30

A researcher runs a regression equation and finds the slope to be significant at the p<.05 level. He then runs the same regression twice, once with the men in the sample, once with the women in the sample. Although both of these new slopes are exactly the same as the original slope, neither of these new slopes is statistically significant. Explain what likely happened.

Question 31

Someone looks at their SPSS regression output, and it says that the significance of their slope is .000. They take this to mean that they can be 100% certain that their slope is statistically significant. Explain to them why they are incorrect in this assumption.

Question 32

A general rule people follow with large samples is: if the slope is twice as large as the standard error of the slope, then the slope is statistically significant. Explain where this rule comes from.

Question 33

A researcher takes a random sample of 10 people and calculates regression results, getting a p-value of 0.052: frustratingly close to statistical significance. To achieve statistical significance, the researcher takes a new, slightly larger sample of 15 people. She now gets a p-value of 0.087. Explain to the researcher what might have happened.

Question 34

What is Ansell's major finding in his research on attitudes toward social security spending?

Question 35

Explain how the Downey article on family size and child's grades offers a contrast between statistical significance and substantive significance.