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Q. 23

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The Practice of Statistics for AP

Found in: Page 764

Book edition 4th

Author(s) David Moore,Daren Starnes,Dan Yates

Pages 809 pages

ISBN 9781319113339

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Short Answer

The slope $β$ of the population regression line describes
(a) the exact increase in the selling price of an individual unit when its appraised value increases by $$ 1000$
(b) the average increase in the appraised value in a population of units when the selling price increases by $51000.
(c) the average increase in selling price in a population of units when the appraised value increases by $ 1000.
(d) the average selling price in a population of units when a unit's appraised value is 0.
(e) the average increase in appraised value in a sample of 16 units when the selling price increases by $ 1000.

(c) the average increase in selling price in a population of units when the appraised value increases by $ 1000.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given Information

Need to find the slope of the population regression.

Step 2: Explanation

In general: The slope of the population regression line is the average increase of y as x increases by 1.

Since y is the actual selling price in thousands of dollars and x is the appraised market value in thousands of dollars, the correct answer then has to be (c).

Most popular questions for Math Textbooks

A large machine is filled with thousands of small

pieces of candy, $40 %$ of which are orange. When money

is deposited, the machine dispenses $60$ randomly selected

pieces of candy. The machine will be recalibrated if a

group of $60$ candies contains fewer than $18$ that are

orange. What is the approximate probability that this will

happen?

$a) P (z < \frac{0.3 - 0.4}{\sqrt{\frac{(0.4) (0.6)}{60}}})$

$b) P (z < \frac{0.4 - 0.3}{\sqrt{\frac{(0.3) (0.7)}{60}}})$

role="math" localid="1650519113387" $c) P (z < \frac{0.3 - 0.4}{\frac{\sqrt{(0.4) (0.6)}}{60}})$

role="math" localid="1650519757907" $d) P (z < \frac{0.3 - 0.4}{\frac{(0.4) (0.6)}{\sqrt{60}}})$

$e) P (z < \frac{0.4 - 0.3}{\frac{\sqrt{(0.3) (0.7})}{60}})$

A residual plot from the least-squares regression is shown below. Which of the following statements is supported by the graph

(a) The residual plot contains dramatic evidence that the standard deviation of the response about the population regression line increases as the average number of putts per round increases.

(b) The sum of the residuals is not 0. Obviously, there is a major error present.

(c) Using the regression line to predict a player’s total winnings from his average number of putts almost always results in errors of less than $$ 200, 000$ .

(d) For two players, the regression line under predicts their total winnings by more than $$ 800, 000$ .

(e) The residual plot reveals a strong positive correlation between average putts per round and prediction errors from the least-squares line for these players.

Suppose a name-brand drug has been deemed effective for reducing hypertension (high blood pressure). The developing company gets to keep a patent on the drug for a specific period of time before other companies can develop a generic form of the drug. Suppose the patent period is about to expire, and another company produces a generic version of this drug. The Food and Drug Administration (FDA) wants to know whether the generic drug is at least as effective as the name-brand drug in reducing blood pressure.

The following hypotheses will be used:

$H_{0} : μ_{g} = μ_{n}$ vs $H_{a} : μ_{g} < μ_{n}$

where

$μ_{g} =$ true mean reduction in blood pressure using the generic drug

$μ_{n} =$ true mean reduction in blood pressure using the name-brand drug. In the context of this situation, which of the following describes a Type I error?

(a) The FDA finds sufficient evidence that the generic drug does not reduce blood pressure as much as the namebrand drug when, in fact, it does not.

(b) The FDA finds sufficient evidence that the generic drug does not reduce blood pressure as much as the namebrand drug when, in fact, it does.

(c) The FDA finds sufficient evidence that the generic drug does reduce blood pressure as much as the namebrand drug when, in fact, it does not.

(d) The FDA finds sufficient evidence that the generic drug does reduce blood pressure as much as the namebrand drug when, in fact, it does.

(e) The FDA does not find sufficient evidence that the generic drug is as effective in reducing blood pressure as the name-brand drug when, in fact, it is.

A set of $10$ cards consists of $5$ red cards and $5$ black cards. The cards are shufﬂed thoroughly, and you choose one at random, observe its color, and replace it in the set. The cards are thoroughly reshufﬂed, and you again choose a card at random, observe its color, and replace it in the set. This is done a total of four times. Let $X$ be the number of red cards observed in these four trials.

The random variable $X$ has which of the following probability distributions?

(a) The Normal distribution with mean $2$ and standard deviation $1$

(b) The binomial distribution with $n = 10$ and role="math" localid="1650534915843" $p = 0.5$

(c) The binomial distribution with $n = 5$ and $p = 0.5$

(d) The binomial distribution with $n = 4$ and $p = 0.5$

(e) The geometric distribution with $p = 0.5$

Following the debut of the new SAT Writing test in March $2005$ , Dr. Les Perelman from the Massachusetts Institute of Technology collected data from a set of sample essays provided by the College Board. A least-squares regression analysis was performed on these data. The two graphs below display the results of that analysis. Explain why the conditions for performing inference are not met in this setting.

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