Log In Start studying!

Select your language

Suggested languages for you:

Americas

English (US)

Europe

Q. 5

Expert-verified

The Practice of Statistics for AP

Found in: Page 692

Book edition 4th

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

Pages 809 pages

ISBN 9781319113339

Answers without the blur.

Just sign up for free and you're in.

Register for Free I’ll do it later

Short Answer

Refer to Exercises 1 and 3.
(a) Confirm that the expected counts are large enough to use a chi-square distribution. Which distribution (specify the degrees of freedom) should you use?
(b) Sketch a graph like Figure 11.4 (page 683) that shows the P-value.
(c) Use Table C to find the P-value. Then use your calculator’s C2cdf command
(d) What conclusion would you draw about the company’s claimed distribution for its deluxe mixed nuts? Justify your answer.

(a) The degree of freedom is 3 and we will use chi- square distribution.

(b)

(c) The value of $p$ is $0.086$

(d) There is insufficient evidence to dismiss the company's claim.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Part (a) Step 1: Given Information

Given in the question to refer exercise 1 and 3.

The projected counts must be large enough for the chi-square distribution to be used. We have to calculate the degree of freedom as well.

Part (a) Step 2: Explanation

To calculate the degree of freedom, use the following formula:

Freedom of degree = number of categories $- 1$ .

The predicted counts can be calculated as follows:

$E (Cashews) = 150 \times (0.52) = 78$

$E (A l m o n d s) = 150 \times (0.27) = 40.5$

$E (Macadamia) = 150 \times (0.13) = 19.5$

$E (Brazil) = 150 \times (0.08) = 12$

If ALL predicted counts are at least $5$ , the expected counts are large enough to employ a chi-square distribution.

The degree of freedom is as follows:

$d f = C - 1 = 4 - 1 = 3$

Part (b) Step 1: Given Information

According to the information, we know that the test statistic is $6.5988$ .

We must create a graph that displays the p value.

Part (b) Step 2: Explanation

From Part (a), we observed that the degree of freedom is $3 .$

As a result, the Chi-square distribution with three degrees of freedom must be used. The P-value is the possibility of winning the test statistic's value, or a number that is more extreme.

Part (c) Step 1: Given Information

According to the information, $χ^{2} = 6.5988$

Using a table and calculator, we must calculate the P-value.

Part (c) Step 2: Explanation

Using the table, the $p$ value at 2 degrees of freedom is:

$P - value = P (χ^{2} > |χ_{Statistic}^{2}|)$

$= P (χ^{2} > 6.5988)$

$= 0.086$

Let's use the Ti-83 calculator to find the $p$ value:

Part (d) Step 1: Given Information

From the previous part, we know that the $χ^{2} = 6.5988$ .

We must reach a conclusion regarding the company's claim.

Part (d) Step 2: Explanation

The significance level is exceeded by the $P -$ value. The null hypothesis is un rejectable. As a result, there is lack of evidence to dismiss the company's distribution claim for its deluxe mixed nuts.

Most popular questions for Math Textbooks

Housing According to the Census Bureau, the distribution by ethnic background of the New York City population in a recent year was

The manager of a large housing complex in the city wonders whether the distribution by the race of the complex’s residents is consistent with the population distribution. To ﬁnd out, she records data from a random sample of $800$ residents. The table below displays the sample data

Are these data signiﬁcantly different from the city’s distribution by race? Carry out an appropriate test at the $α = 0.05$ level to support your answer. If you ﬁnd a signiﬁcant result, perform follow-up analysis.

No answer $(4.1)$ Explain carefully how nonresponse could lead to bias in this project

The expected count of females who respond “almost certain” is

(a) $464.6$ .

(b) $891.2$ .

(c) $1038.8$ .

(d) $1174$ .

(e) None of these.

The cell in the table that contributes the most to the chi-square statistic is (a) Female, $50 - 50$ chance.

(b) Male, $50 - 50$ chance.

(c) Female, almost certain.

(d) Male, almost certain.

(e) All the cells contribute equally to the test statistic.

Reading and grades (3.2) The Fathom scatterplot below show the number of books read and the English grade for all $79$ students in the study. A least-squares regression line has been added to the graph.

(a) Interpret the meaning of the y-intercept in context.

(b) The student who reported reading $17$ books for pleasure had an English GPA of $2.85$ . Find this student’s residual. Show your work.

(c) How strong is the relationship between English grades and the number of books read? Give appropriate evidence to support your answer.

Want to see more solutions like these?

Sign up for free to discover our expert answers

Get Started - It’s free

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free