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Q.1

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The Practice of Statistics for AP

Found in: Page 621

Book edition 4th

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

Pages 809 pages

ISBN 9781319113339

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Short Answer

Toyota or Nissan? Are Toyota or Nissan owners more satisﬁed with their vehicles? Let’s design a study to ﬁnd out. We’ll select a random sample of $400$ Toyota owners and a separate random sample of $400$ Nissan owners. Then we’ll ask each individual in the sample: “Would you say that you are generally satisﬁed with your (Toyota/Nissan) vehicle?”
(a) Is this a problem with comparing means or comparing proportions? Explain.
(b) What type of study design is being used to produce data?

From the given information,

a) The problem is about comparing proportions.

b) Observational study is being used to produce data.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Part (a) Step 1: Given Information

We should structure an examination to discover. Well, select an arbitrary example Of Toyota proprietors and a different irregular example of $400$ Nissan proprietors.

Part (a) Step 2: Explanation

Heretofore, two categories are involved in this problem, that is, Yes or No. It means that the collected data is categorical the mean cannot be computed here. Thus, it could not be completed that the problem is about proportions.

Part (b) Step 3: Given Information

It is given in the question, What type of study design is being used to produce data?

Part (b) Step 4: Explanation

Heretofore the observational study does not affect the outcome and in the supplied case no outcomes have been influenced here. Therefore, the study is observational.

Most popular questions for Math Textbooks

The Environmental Protection Agency is charged with monitoring industrial emissions that pollute the atmosphere and water. So long as emission levels stay within specified guidelines, the EPA does not take action against the polluter. If the polluter is in violation of the regulations, the offender can be fined, forced to clean up the problem, or possibly closed. Suppose that for a particular industry the acceptable emission level has been set at no more than $5$ parts per million ( $5$ ppm). The null and alternative hypotheses are $H_{0}$ role="math" localid="1650298159260" $: μ = 5$ versus $H_{a} = μ > 5$ . Which of the following describes a Type II error?

(a) The EPA fails to find evidence that emissions exceed acceptable limits when, in fact, they are within acceptable limits.

(b) The EPA concludes that emissions exceed acceptable limits when, in fact, they are within acceptable limits.

(c) The EPA concludes that emissions exceed acceptable limits when, in fact, they do exceed acceptable limits.

(d) The EPA takes more samples to ensure that they make the correct decision.

(e) The EPA fails to find evidence that emissions exceed acceptable limits when, in fact, they do exceed acceptable limits.

A sample survey interviews SRSs of $500$ female college students and $550$ male college students. Each student is asked whether he or she worked for pay last summer. In all, $410$ of the women and $484$ of the men say “Yes.” The $95 %$ confidence interval for the difference $p_{M} - p_{F}$ in the proportions of college men and women who worked last summer is about

(a) $0.06 \pm 0.00095$

(b) $0.06 \pm 0.043 .$

(c) $0.06 \pm 0.036$

(d) $- 0.06 \pm 0.043$

(e) $- 0.06 \pm 0.036$

Thirty-five people from a random sample of $125$ workers from Company A admitted to using sick leave when they weren’t really ill. Seventeen employees from a random sample of $68$ workers from Company B admitted that they had used sick leave when they weren’t ill. A 95% confidence interval for the difference in the proportions of workers at the two companies who would admit to using sick leave when they weren’t ill is

(a) $0.03 \pm \sqrt{\frac{(0.28) (0.72)}{125} + \frac{(0.25) (0.75)}{68}}$

(b) localid="1650367573248" $0.03 \pm 1.96 \sqrt{\frac{(0.28) (0.72)}{125} + \frac{(0.25) (0.75)}{68}}$

(c) $0.03 \pm 1.645 \sqrt{\frac{(0.28) (0.72)}{125} + \frac{(0.25) (0.75)}{68}}$

(d)

$0.03 \pm 1.96 \sqrt{\frac{(0.269) (0.731)}{125} + \frac{(0.269) (0.731)}{68}}$

(e) $0.03 \pm 1.645 \sqrt{\frac{(0.269) (0.731)}{125} + \frac{(0.269) (0.731)}{68}}$

Find the mean and standard deviation of the sampling distribution. Show your work.

A random sample of 100 of a certain popular car model last year found that 20 had a certain minor defect in the brakes. The car company made an adjustment in the production process to try to reduce the proportion of cars with the brake problem. A random sample of 350 of this year's model found that 50 had the minor brake defect.

(a) Was the company's adjustment successful? Carry out an appropriate test to support your answer.

(b) Describe a Type I error and a Type Il error in this setting, and give al possible consequence of each.

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