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AP Statistics - CIS: CI for Slopes
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AP Statistics - CIS: CI for Slopes 0/5
Question 1 of 5   |  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
\(11.8204 \pm 1.645(1.848)\)
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B
\(11.8204 \pm 1.711(1.848)\)
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C
\(11.8204 \pm 1.714(1.848)\)
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D
\(11.8204 \pm \dfrac{1.645(1.848)}{\sqrt{25}}\)
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E
\(11.8204 \pm \dfrac{1.711(1.848)}{\sqrt{25}}\)
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Question 2 of 5   |  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
\(9{,}718 \pm 2.054\)
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B
\(9{,}718 \pm 2.197\)
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C
\(9{,}718 \pm 2.214\left(\dfrac{7{,}208}{\sqrt{20}}\right)\)
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D
\(15{,}675 \pm 2.197\left(\dfrac{15{,}720}{\sqrt{20}}\right)\)
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E
\(15{,}675 \pm 2.214(1{,}678)\)
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Question 3 of 5   |  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
\(410.997 \pm 1.771(67.79)\)
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B
\(410.997 \pm 1.796(67.79)\)
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C
\(5.52979 \pm 1.645(74.29)\)
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D
\(5.52979 \pm 1.771(1.135)\)
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E
\(5.52979 \pm 1.796(1.135)\)
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Question 4 of 5   |  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.
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B
We are 95 percent confident that for each \(1000 more \in salary t hat an alumnus earns, \dfrac{he}{she} will donate between \)\(12.01 more.\)
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C
We are 95 percent confident that for each \(1000 more \in salary t hat an alumnus earns, it is predicted t hat \dfrac{he}{she} will donate between \)\(12.01 more on average.\)
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D
89.8 percent of the variability in gift donations is explained by the linear model.
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E
89.8 percent of the variability in gift donations is explained by variability in salary.
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Question 5 of 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.
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B
The probability is 0.92 that, on average, each additional page will raise the price \$0.15.
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C
92 percent of all random samples of textbooks will give a regression slope between 0.115 and 0.185.
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D
We are 92 percent confident that each additional page will raise the price \$0.15.
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E
We are 92 percent confident that each additional page will raise the price between \$0.115 and \$0.185 on average.
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Graphing Calculator
Reference Sheet

Area & Circumference

Circle$A = \pi r^2$,  $C = 2\pi r$
Rectangle$A = lw$
Triangle$A = \tfrac{1}{2}bh$
Trapezoid$A = \tfrac{1}{2}(b_1+b_2)h$

Volume

Box$V = lwh$
Cylinder$V = \pi r^2 h$
Sphere$V = \tfrac{4}{3}\pi r^3$
Cone$V = \tfrac{1}{3}\pi r^2 h$
Pyramid$V = \tfrac{1}{3}lwh$

Triangles

Pythagorean Thm$a^2 + b^2 = c^2$
30-60-90sides: $1,\, \sqrt{3},\, 2$
45-45-90sides: $1,\, 1,\, \sqrt{2}$
Triangle Anglessum $= 180°$

Other Facts

Circle Degrees$360° = 2\pi \text{ rad}$
Exterior Angle= sum of non-adjacent interior angles

The number of degrees of arc in a circle is 360. The number of radians of arc in a circle is $2\pi$.

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