AP Statistics with 6 Practice Tests

Martin Sternstein

Chapter 9

Inference for Quantitative Data: Slopes - all with Video Answers

Educators

Section 31

Quiz 31

Problem 1

Inference about the slope of a least squares regression line is based on the sampling distribution of $b$ being
(A) approximately normal.
(B) a chi-square distribution with $d f=n-1$.
(C) a chi-square distribution with $d f=n-2$.
(D) a $t$ -distribution with $d f=n-1$.
(E) a $t$ -distribution with $d f=n-2$.

Harsh Gadhiya

Harsh Gadhiya

Numerade Educator

Problem 2

A statistician investigated the relationship between ages and bowling scores for participants in an adult bowling league. The regression analysis for her data is shown below.
By how much do bowling score estimates produced by this model typically differ from the actual scores of the bowlers?
(A) 1.200
(B) 3.342
(C) 37.3598
(D) 94.44
(E) 122.79

Meredith Kempson

Meredith Kempson

Numerade Educator

Problem 3

A statistician wonders if dress size can be predicted from a woman's height. In a random sample of 20 female high school students, dress size versus height $(\mathrm{cm})$ gives the following regression results:
Is there statistical evidence of a linear relationship between dress size and height $\left(H_{0}: \beta=0, H_{\mathrm{a}}: \beta \neq 0\right) ?$
(A) No, because $r^{2}$, the coefficient of determination, is too small.
(B) No, because 0.128 is above any reasonable significance level.
(C) Yes, because by any reasonable observation, taller women tend to have larger dress sizes.
(D) Yes, because the computer printout does give a regression equation.
(E) There is sufficient evidence at the $10 \%$ significance level but not at the $5 \%$ level.

Harsh Gadhiya

Numerade Educator

Problem 4

A $95 \%$ confidence interval for the slope of a regression line is calculated to be $(-0.783,0.457) .$ Which of the following must
be true?
(A) The slope of the regression line is o.
(B) The slope of the regression line is -0.326 .
(C) A scatterplot of the data would show a linear pattern.
(D) A residual plot would show no pattern.
(E) The correlation is negative.

Meredith Kempson

Meredith Kempson

Numerade Educator

Problem 5

Refer to the following setting. In a random sample of 25 professional baseball players, their salaries (in millions of dollars) and batting averages result in the following regression analysis:
What is the equation of the least squares regression line?
(A) Batting Average $=0.008051+0.2336$ (Salary)
(B) Predicted Batting Average $=0.008051+0.2236$ (Salary)
(C) Predicted Batting Average $=0.2336+0.008051($ Salary)
(D) Predicted Batting Average $=0.002825+$ 0.008051(Salary)
(E) Predicted Salary $=0.2336+0.008051$ (Batting Average)

Harsh Gadhiya

Numerade Educator

Problem 6

Refer to the following setting. In a random sample of 25 professional baseball players, their salaries (in millions of dollars) and batting averages result in the following regression analysis:
Which of the following gives a 95 percent confidence interval for the slope of the regression line?
(A) $0.008051 \pm 1.96(0.002825)$
(B) $0.008051 \pm 1.96(0.01695)$
(C) $0.008051 \pm 2.0639(0.002825)$
(D) $0.008051 \pm 2.0687(0.002825)$
(E) $0.008051 \pm 2.85(0.002825)$

Meredith Kempson

Meredith Kempson

Numerade Educator

Problem 7

Refer to the following setting. In a random sample of 25 professional baseball players, their salaries (in millions of dollars) and batting averages result in the following regression analysis:
In testing the hypothesis $H_{0}: \beta=0$ versus $H_{\mathrm{a}}: \beta>0,$ what is the $t$ -statistic?
(A) 2.850
(B) (0.5)(2.850)
(C) 39.71
(D) (0.5)(39.71)
(E) This cannot be answered without first deciding on an $\alpha$ risk.

Meredith Kempson

Meredith Kempson

Numerade Educator

Problem 8

Refer to the following setting. In a random sample of 25 professional baseball players, their salaries (in millions of dollars) and batting averages result in the following regression analysis:
In testing the hypothesis $H_{0}: \beta=0$ versus $H_{\mathrm{a}}: \beta>0,$ what is
the $P$ -value?
(A) 0.0045
(B) 0.0091
(C) 0.0250
(D) 0.7030
(E) 0.7160

Meredith Kempson

Meredith Kempson

Numerade Educator