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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

Men versus women The National Assessment of Educational Progress (NAEP)

Young Adult Literacy Assessment Survey interviewed separate random samples of $840$

men and $1077$ women aged $21$ to $25$ years.

The mean and standard deviation of scores on the NAEP’s test of quantitative skills were x1= $272.40$ and s1= $59.2$ for the men in the sample. For the women, the results were x ̄2= $274.73$ and s2= $57.5$ .

a. Construct and interpret a $90$ % confidence interval for the difference in mean score for

male and female young adults.

b. Based only on the interval from part (a), is there convincing evidence of a difference

in mean score for male and female young adults?

Literacy Refer to Exercise 2.

a. Find the probability that the proportion of graduates who pass the test is at most $0.20$ higher than the proportion of dropouts who pass, assuming that the researcher’s report is correct.

b. Suppose that the difference (Graduate – Dropout) in the sample proportions who pass the test is exactly $0.20$ . Based on your result in part (a), would this give you reason to doubt the researcher’s claim? Explain your reasoning.

Bag lunch? Phoebe has a hunch that older students at her very large high

school are more likely to bring a bag lunch than younger students because they have grown tired of cafeteria food. She takes a simple random sample of 80 sophomores and finds that $52$ of them bring a bag lunch. A simple random sample of $104$ seniors reveals that $78$ of them bring a bag lunch.

a. Do these data give convincing evidence to support Phoebe’s hunch at the $α = 0.05$ significance level?

b. Interpret the $P$ -value from part (a) in the context of this study.

In an experiment to learn whether substance M can help restore memory, the brains of $20$ rats were treated to damage their memories. First, the rats were trained to run a maze. After a day, $10$ rats (determined at random) were given substance M and $7$ of them succeeded in the maze. Only $2$ of the $10$ control rats were successful. The two-sample z test for the difference in the true proportions

a. gives $z = 2.25, P < 0.02$ .

b. gives $z = 2.60, P < 0.005$ .

c. gives $z = 2.25, P < 0.04$ but not $< 0.02$

d. should not be used because the Random condition is violated.

e. should not be used because the Large Counts condition is violated.

Mrs. Woods and Mrs. Bryan are avid vegetable gardeners. They use different fertilizers, and each claims that hers is the best fertilizer to use when growing tomatoes. Both agree to do a study using the weight of their tomatoes as the response variable. Each planted the same varieties of tomatoes on the same day and fertilized the plants on the same schedule throughout the growing season. At harvest time, each randomly selects $15$ tomatoes from her garden and weighs them. After performing a two-sample t test on the difference in mean weights of tomatoes, they get $t = 5.24$ and $P = 0.0008$ . Can the gardener with the larger mean claim that her fertilizer caused her tomatoes to be heavier?

a. Yes, because a different fertilizer was used on each garden.

b. Yes, because random samples were taken from each garden.

c. Yes, because the P-value is so small.

d. No, because the condition of the soil in the two gardens is a potential confounding variable.

e. No, because $15 < 30$

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