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AP Statistics - CIS: CI for Slopes

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1 Statistical Inference > CI for slopes · Level 3
Below is the computer output for a regression analysis involving starting salary (in \$1,000) and college GPA in a random sample of 25 graduates. What is a 90% confidence interval for the slope of the regression line?
A
\(11.8204 \pm 1.645(1.848)\)
B
\(11.8204 \pm 1.711(1.848)\)
C
\(11.8204 \pm 1.714(1.848)\)
D
\(11.8204 \pm \dfrac{1.645(1.848)}{\sqrt{25}}\)
E
\(11.8204 \pm \dfrac{1.711(1.848)}{\sqrt{25}}\)
2 Statistical Inference > CI for slopes · Level 3
An insurance adjustor is interested in the age of homes and average wind and flood damage from hurricanes. Data from 20 randomly selected homes generate the following computer output: Which of the following gives a 96% confidence interval for the slope of the regression line?
A
\(9{,}718 \pm 2.054\)
B
\(9{,}718 \pm 2.197\)
C
\(9{,}718 \pm 2.214\left(\dfrac{7{}{}208, \sqrt{20}}\right)\)
D
\(15{,}675 \pm 2.197\left(\dfrac{15{}{}720, \sqrt{20}}\right)\)
E
\(15{,}675 \pm 2.214(1{,}678)\)
3 Statistical Inference > CI for slopes · Level 3
A study is made relating life expectancy (in days) of a laptop battery as a function of price of the battery. Data from a sample of 13 laptops generates the following computer output. Which of the following gives a 90% confidence interval for the slope of the regression line?
A
\(410.997 \pm 1.771(67.79)\)
B
\(410.997 \pm 1.796(67.79)\)
C
\(5.52979 \pm 1.645(74.29)\)
D
\(5.52979 \pm 1.771(1.135)\)
E
\(5.52979 \pm 1.796(1.135)\)
4 Statistical Inference > CI for slopes · Level 3
A college Office of Alumni Relations gathers data and performs a linear regression analysis on donation gifts versus salary of alumni. The resulting computer output (where salary is in \$1,000) is shown below. What is a 95% confidence interval of the slope interpreted in context?
A
We are 95 percent confident that for each \(1000 more \in salary t hat an alumnus earns, \dfrac{he}{she} will donate \)10.29 more.
B
We are 95 percent confident that for each \(1000 more \in salary t hat an alumnus earns, \dfrac{he}{she} will donate between \)8.57 and \$12.01 more.
C
We are 95 percent confident that for each \(1000 more \in salary t hat an alumnus earns, it is predicted t hat \dfrac{he}{she} will donate between \)8.57 and \$12.01 more on average.
D
89.8 percent of the variability in gift donations is explained by the linear model.
E
89.8 percent of the variability in gift donations is explained by variability in salary.
5 Statistical Inference > CI for slopes · Level 3
A regression analysis of the prices of textbooks versus page lengths yields the following equation. Predicted price = \(-3.35 + 0.15\)(Pages) A 92% confidence interval of the slope is (0.115, 0.185). What is a correct interpretation of this interval in context?
A
Every additional page will raise the price \$0.15.
B
The probability is 0.92 that, on average, each additional page will raise the price \$0.15.
C
92 percent of all random samples of textbooks will give a regression slope between 0.115 and 0.185.
D
We are 92 percent confident that each additional page will raise the price \$0.15.
E
We are 92 percent confident that each additional page will raise the price between \$0.115 and \$0.185 on average.
6 Statistical Inference > CI for slopes · Level 3
The 96% confidence interval for the slope of a regression line is (\(-0.142\), \$1.036). Which of the following is a true statement?
A
The sample slope is \(b = 0\).
B
The sample slope is \(b = 0.589\).
C
The sum of the residuals is positive.
D
The mean of the residuals is positive.
E
The correlation coefficient \(r\) is positive.

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