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The Practice of Statistics for AP

David Moore,Daren Starnes,Dan Yates

$Math Studyset Vaia Explanations$ Math

4th Edition · 809 pages

ISBN: 9781319113339

Chapter 12: Q. 24 (page 764)

Is there significant evidence that selling price increases as appraised value increases? To answer this question, test the hypotheses
(a) $H_{0} : β = 0 versus H_{a} : β > 0 .$ .
(b) $H_{0} : β = 0 versus H_{a} : β < 0$
(c) $H_{0} : β = 0 versus H_{a} : β \neq 0$
(d) $H_{0} : β > 0 versus H_{a} = β = 0 .$
(e) $H_{x : β} = 1 versus. H \cdot θ > 1$

Short Answer

Expert verified

$(a) H_{0} : β = 0 versus H_{a} : β > 0 .$

Step by step solution

01

Given Information

Need to test the hypothesis.

02

Explanation

Claim: Is there an increase? Or equivalently, Is the slope of the population regression line positive?

The null hypothesis states that the population parameter is equal to the value mentioned in the claim:

H_{0} : β = 0

The alternative hypothesis states the opposite of the null hypothesis (according to the claim):

H_{a} : β > 0

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Most popular questions from this chapter

Brawn versus brain How is the weight of an animal's brain related to the weight of its body?

Researchers collected data on the brain weight (in grams) and body weight (in kilograms) for $96$ species of mammals. The figure below is a scatterplot of the logarithm of brain weight against the logarithm of body weight for all $96$ species. The least-squares regression line for the transformed data is

$\hat{\log y} = 1.01 + 0.72 \log x$

Based on footprints and some other sketchy evidence, some people think that a large apelike animal, called Sasquatch or Bigfoot, lives in the Pacific Northwest. His weight is estimated to be about $280$ pounds, or $127$ kilograms. How big is Bigfoot’s brain? Show your method clearly

Beer and BAC How well does the number of beers a person drinks predict his or her blood alcohol content (BAC)? Sixteen volunteers with an initial BAC of $0$ drank a randomly assigned number of cans of beer. Thirty minutes later, a police officer measured their BAC. Least-squares regression was performed on the data. A residual plot and a histogram of the residuals are shown below. Check whether the conditions for performing inference about the regression model are met.

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

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

What is the correlation between the selling price and appraised value?

(a) 0.1126

(c) -0.861

(e) -0.928

(b) 0.861

(d) 0.928

A distribution of exam scores has mean $60$ and standard deviation $18$ . If each score is doubled, and then $5$ is subtracted from that result, what will be the mean and standard deviation, respectively, of the new scores?

(a) mean $= 115$ and standard deviation $= 31$

(b) mean $= 115$ and standard deviation $= 36$

(c) mean $= 120$ and standard deviation $= 6$

(d) mean $= 120$ and standard deviation $= 31$

(e) mean $= 120$ and standard deviation $= 36$

See all solutions

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