Question 1

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

Accepted Answer

Each building block in the distribution is a sample slope, created by taking a sample from the population and calculating the slope of the regression line for that sample.

Question 2

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

Accepted Answer

The p-value in inference with regression represents the probability that the population slope is zero. This is because the null hypothesis in regression analysis is that the population slope is equal to zero. The p-value tells us the strength of evidence against this null hypothesis, with a low p-value indicating that it is unlikely that the population slope is zero.

Question 3

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

Accepted Answer

C

Question 4

Everything else remaining constant, the larger the sample size:

Accepted Answer

The larger the sample size, the more representative the sample is of the population, and therefore the smaller the standard error (the measure of the variability of sample mean from the population mean).

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?

Accepted Answer

To achieve statistical significance at a common level (e.g., 5%), the slope divided by the standard error should be greater than approximately 2 (the critical value for large samples). Thus, the slope should be greater than 4 (2 * 2).

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?

Accepted Answer

If the value of the slope and the standard error are the same, then the t-value is 1, which is nowhere near the 1.96 that we would need to reach for statistical significance.

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?

Accepted Answer

We divide the slope by the standard error and get 4.75, which is larger than the 3.29 we need to move to p<.001.

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?

Accepted Answer

We divide the slope by the standard error and get 1.89, which is not quite high enough to say that p<.05, so we must conclude that 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:

Accepted Answer

A larger sample with the same slope will at least be as statistically significant as the slopes of the separate samples.

Question 10

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

Accepted Answer

The textbook stresses that statistical significance is strongly affected by the size of the sample, so a larger sample size will enhance statistical significance.

Question 11

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

Accepted Answer

The asterisk symbol (*) is most typically used to represent the statistical significance of a slope. It is commonly used in many statistical software packages and is recognized by researchers as indicating the level of significance for the slope coefficient.

Question 12

Most regression results related to statistical significance are reported as:

Accepted Answer

Two-tailed tests are commonly used in regression analysis to test whether the coefficients are significantly different from zero. This type of test considers both positive and negative deviations from the null hypothesis and is the most appropriate for most regression analyses.

Question 13

The BMI and income example in the textbook found:

Accepted Answer

The answer of The BMI and income example in the...

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 ____________.

Accepted Answer

The example indicates that those born outside the U.S. had a larger slope, but this slope was not statistically significant, meaning the difference in attitudes was not strong enough to be considered meaningful in a statistical sense.

Question 15

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

Accepted Answer

The answer of Which national dataset does Ansell use in...

Question 16

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

Accepted Answer

Ansell's article focuses on the connection between a respondent's support for social security spending and the appreciation of their house value. He posits that as the value of a person's house increases, their personal wealth grows, potentially influencing their views on the need for social security spending.

Question 17

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

Accepted Answer

The answer of Ansell's measure of support for social security...

Question 18

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

Accepted Answer

Ansell's article is noted for its careful description of the actual effect sizes, which provides a clear understanding of the magnitude of the effects discussed.

Question 19

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

Accepted Answer

Downey uses the National Educational Longitudinal Study in his research on the relationship between family size and academic performance.

Question 20

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

Accepted Answer

Downey's regression of family size on grades involved nearly 17,000 cases, indicating a large-scale study that provided a robust dataset for analysis.

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