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The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset Vaia Explanations$ Math

6th Edition · 837 pages

ISBN: 9781319113339

Chapter 10: Q. 3.12 (page 702)

The correlation between the heights of fathers and the heights of their grownup sons, both measured in inches, is $r = 0.52$ . If fathers’ heights were measured in feet instead, the correlation between heights of fathers and heights of sons would be
a. much smaller than $0.52$ .
b. slightly smaller than $0.52$ .
c. unchanged; equal to $0.52$ .
d. slightly larger than $0.52$ .
e. much larger than $0.52$ .

Short Answer

Expert verified

The correlation between heights of fathers and heights of sons would be (c) unchanged; equal to $0.52$ .

Step by step solution

01

Given information

We need to find correlation between heights of fathers and heights of sons if it is measured in feets .

02

Explanation

Here we are given with value of $r = 0.52$

Also , measurement of correlation is unitless , it does not change with changing units ;

Moreover, the value is also arbitary in nature .

Therefore , the correlation between heights of fathers and heights of sons would be unchanged; equal to $0.52$ .

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Most popular questions from this chapter

Researchers suspect that Variety A tomato plants have a different average yield than Variety B tomato plants. To find out, researchers randomly select $10$ Variety A and $10$ Variety B tomato plants. Then the researchers divide in half each of $10$ small plots of land in different locations. For each plot, a coin toss determines which half of the plot gets a Variety A plant; a Variety B plant goes in the other half. After harvest, they compare the yield in pounds for the plants at each location. The $10$ differences (Variety A − Variety B) in yield are recorded. A graph of the differences looks roughly symmetric and single-peaked with no outliers. The mean difference is ${\bar{x}}_{A - B}$ $= 0.34$ $\frac{305}{1526} = 0.200 = 20 % {\bar{x}}_{A - B} = 0.34$ and the standard deviation of the differences is s A-B $= 0.83$ $\frac{305}{1526} = 0.200 = 20 % = s_{A - B} = 0.83$ .Let $μ_{A - B} = \frac{305}{1526} = 0.200 = 20 %$ μA−B = the true mean difference (Variety A − Variety B) in yield for tomato plants of these two varieties.

A 95% confidence interval for $μ_{A - B} \frac{305}{1526} = 0.200 = 20 % μ_{A - B}$ is given by

a. $0.34 \pm 1.96 (0.83) \frac{305}{1526} = 0.200 = 20 % 0.34 \pm 1.96 (0.83)$

b. $0.34 \pm 1.96 (0.8310) \frac{305}{1526} = 0.200 = 20 % 0.34 \pm 1.96 (0.8310)$

c. $0.34 \pm 1.812 (0.8310) \frac{305}{1526} = 0.200 = 20 % 0.34 \pm 1.812 (0.8310)$

d. $0.34 \pm 2.262 (0.83) \frac{305}{1526} = 0.200 = 20 % 0.34 \pm 2.262 (0.83)$

e. $0.34 \pm 2.262 (0.8310) \frac{305}{1526} = 0.200 = 20 % 0.34 \pm 2.262 (0.8310)$

There are two common methods for measuring the concentration of a pollutant in fish tissue. Do the two methods differ, on average? You apply both methods to each fish in a random sample of $18$ carp and use

a. the paired t test for $μ d i f f \frac{305}{1526} = 0.200 = 20.0 % μ d i f f$ .

b. the one-sample z test for p.

c. the two-sample t test for $μ 1 - μ 2 \frac{305}{1526} = 0.200 = 20.0 % μ 1 - μ 2$ .

d. the two-sample z test for $p 1 - p 2 \frac{305}{1526} = 0.200 = 20.0 % p 1 - p 2$ .

e. none of these.

Which of the following statements is false?

a. A measure of center alone does not completely summarize a distribution of quantitative data.

b. If the original measurements are in inches, converting them to centimeters will not change the mean or standard deviation.

c. One of the disadvantages of a histogram is that it doesn’t show each data value.

d. In a quantitative data set, adding a new data value equal to the mean will decrease the standard deviation.

e. If a distribution of quantitative data is strongly skewed, the median and interquartile range should be reported rather than the mean and standard deviation.

Literacy A researcher reports that $80 %$ of high school graduates, but only $40 %$ of high school dropouts, would pass a basic literacy test. Assume that the researcher’s claim is true. Suppose we give a basic literacy test to a random sample of $60$ high school graduates and a separate random sample of $75$ high school dropouts. ${\hat{p}}_{G}, {\hat{p}}_{D}$ be the sample proportions of graduates and dropouts, respectively, who pass the test.

a. What is the shape of the sampling distribution of ${\hat{p}}_{G} - {\hat{p}}_{D}$ . Why?

b. Find the mean of the sampling distribution.

c. Calculate and interpret the standard deviation of the sampling distribution.

Shortly before the $2012$ presidential election, a survey was taken by the school newspaper at a very large state university. Randomly selected students were asked, “Whom do you plan to vote for in the upcoming presidential election?” Here is a two-way table of the responses by political persuasion for $1850$ students:

Candidate of choice	Political persuasion
		Democrat	Republican	Independent	Total
	Obama	$925$	$78$	$26$	$1029$
	Romney	$78$	$598$	$19$	$695$
	Other	$2$	$8$	$11$	$21$
	Undecided	$32$	$28$	$45$	$105$
	Total	$1037$	$712$	$101$	$1850$

Which of the following statements about these data is true?

a. The percent of Republicans among the respondents is $41 % .$

b. The marginal relative frequencies for the variable choice of candidate are given by

Obama: $55.6 %$ ; Romney: $37.6 %$ ; Other: $1.1 %$ ; Undecided: $5.7 %$ .

c. About $11.2 %$ of Democrats reported that they planned to vote for Romney.

d. About $44.6 %$ of those who are undecided are Independents.

e. The distribution of political persuasion among those for whom Romney is the

candidate of choice is Democrat: $7.5 %$ ; Republican: $84.0 %$ ; Independent: $18.8 %$ .

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