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AP Statistics - HTS: Hypothesis Tests for Slopes

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1 Statistical Inference > Hypothesis tests for slopes · Level 3
A retailer believes that sales of some luxury items go up when the price is higher. Below is the computer printout for the regression analysis of sales versus price (in \$1,000s) for a random sample of these luxury items. W hat is the P-value for a t-test with \(H_0: \beta = 0\) and \(H_a: \beta > 0\)?
A
0.0124
B
0.0239
C
0.0478
D
0.0956
E
0.5060
2 Statistical Inference > Hypothesis tests for slopes · Level 3
A linear regression analysis is performed on two variables. Which of the following tells you that another model probably gives a better fit?
A
The correlation r is low.
B
The mean of the residuals is 0.
C
The P-value for \(H_0: \beta = 0\) and \(H_a: \beta > 0\) is low.
D
The coefficient of determination is high.
E
The residual plot has a pattern.
3 Statistical Inference > Hypothesis tests for slopes · Level 3
The space shuttle Challenger took off when the temperature was 31°F. Before this launch, 23 earlier launches experienced from zero to three O-ring failures. After the Challenger disaster, there was some speculation that the number of O-ring failures was related to temperature at liftoff. A computer printout, performed too late, is shown below. Is there evidence of a relationship between O-ring failures and temperature at liftoff?
A
There is no evidence of a relationship between the number of O-ring failures and the temperature at liftoff.
B
There is evidence of a relationship at the 0.10 level but not at the 0.05 level.
C
There is evidence of a relationship at the 0.05 level but not at the 0.01 level.
D
There is evidence of a relationship at the 0.01 level but not at the 0.001 level.
E
There is evidence of a relationship at the 0.001 level.
4 Statistical Inference > Hypothesis tests for slopes · Level 3
In a random sample of 20 college students, each was interviewed as to GPA and weekly work-study hours on campus. What is the critical t-value in calculating a 95% confidence interval estimate for the slope of the resulting least squares regression line?
A
1.96
B
2.074
C
2.086
D
2.093
E
2.101
5 Statistical Inference > Hypothesis tests for slopes · Level 3
A scatterplot of the ages of 30 couples applying for marriage licenses shows a strong, positive, linear relationship between the men's and women's ages. A significance test on the slope with \(H_0: \beta = 0\) and \(H_a: \beta > 0\) results in a P-value of 0.035. Which of the following statements is an appropriate conclusion?
A
With this small of a P-value, 0.035 < 0.05, there is not sufficient evidence of a linear relationship between the men's and women's ages of couples applying for marriage licenses.
B
With this small of a P-value, 0.035 < 0.05, there is proof of a linear relationship between the men's and women's ages of couples applying for marriage licenses.
C
With this small of a P-value, 0.035 < 0.05, there is sufficient evidence that among couples applying for marriage licenses, a one-year difference in ages among men corresponds to a constant positive difference in ages among women on average.
D
Among couples applying for marriage licenses, 3.5 percent of the difference among the women's ages can be explained by the linear model of women's ages versus men's ages.
E
Among couples applying for marriage licenses, 12.25 percent of the difference among the women's ages can be explained by the linear model of women's ages versus men's ages.
6 Statistical Inference > Hypothesis tests for slopes · Level 3
An auto magazine report analyzes the association between the weight of a car (in thousands of pounds) and the fuel efficiency (in miles per gallon). Some of the regression analysis is shown below. Assuming that all conditions for inference are met, what is the appropriate test statistic for testing the null hypothesis, \(H_0: \beta = 0\), that the slope of the regression line is 0?
A
\(\dfrac{45.7}{2.01}\)
B
\(\dfrac{24.1}{0.867}\)
C
\(\dfrac{-8.73}{2.39}\)
D
\(\dfrac{-8.73}{0.74}\)
E
\(\dfrac{-8.73}{(0.74)\sqrt{30}}\) QUESTIONS 5

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