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Q. 7

Expert-verified

The Practice of Statistics for AP

Found in: Page 734

Book edition 4th

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

Pages 809 pages

ISBN 9781319113339

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Short Answer

The appropriate degrees of freedom for the $x^{2}$ statistic is
(a) 1 .
(b) 2 .
(c) 3 .
(d) 4 .
(e) 5 .

Option $(b)$ is the correct answer.

The appropriate degrees of freedom for the $x^{2}$ statistic is $2$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given Information

Need to find The appropriate degrees of freedom for the $x^{2}$ statistic .

Step 2: Explanation

The number of columns in the given table is:

$c = 3$

The number of rows in the given table is:

$r = 2$

The number of degrees of freedom is the product of the number of columns decreased by 1 and the number of rows decreased by 1.

localid="1650541311764" $d f = (c - 1) (r - 1) = (2 - 1) (3 - 1) = (1) (2) = 2$

Most popular questions for Math Textbooks

Canada has universal health care. The United States does not but often offers more elaborate treatment to patients with access. How do the two systems compare in treating heart attacks? Researchers compared random samples of $2600$ U.S. and $400$ Canadian heart attack patients. One key outcome was the patients’ own assessment of their quality of life relative to what it had been before the heart attack. Here are the data for the patients who survived a year:

$\begin{matrix} Quality of life & Canada & United States \\ Much better & 75 & 541 \\ Somewhat better & 71 & 498 \\ About the same & 96 & 779 \\ Somewhat worse & 50 & 282 \\ Much worse & 19 & 65 \\ Total & 311 & 2165 \end{matrix}$

Construct an appropriate graph to compare the distributions of opinions about the quality of life among heart attack patients in Canada and the United States.

Calculate the chi-square statistic. Show your work.

How do U.S. residents who travel overseas for leisure differ from those who travel for business? The following is the breakdown by occupation:

Explain why we can’t use a chi-square test to learn whether these two distributions differ significantly.

Refer to Exercise 27. Do the data provide convincing evidence of a difference in the distributions of sports goals for male and female undergraduates at the university?

(a) State appropriate null and alternative hypotheses for a significance test to help answer this question.

(b) Calculate the expected counts. Show your work.

(c) Calculate the chi-square statistic. Show your work

From exercise $27$

Mars, Inc., reports that their M&M’S Peanut Chocolate Candies are produced according to the following color distribution: 23% each of blue and orange, 15% each of green and yellow, and 12% each of red and brown. Joey bought a bag of Peanut Chocolate Candies and counted the colors of the candies in his sample: 12 blue, 7 orange, 13 green, 4 yellow, 8 red, and 2 brown.

Calculate the expected count for each color, assuming that the company’s claim is true. Show your work.

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