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Q.10

Expert-verified

The Practice of Statistics for AP

Found in: Page 482

Book edition 4th

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

Pages 809 pages

ISBN 9781319113339

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Short Answer

How confident? The figure at top right shows the result of taking $25$ SRSs from a Normal population and constructing a confidence interval for each sample. Which confidence level— $80 %, 90 %, 95 %$ , or $99 %$ —do you think was used? Explain.

The nearest confidence level is $99 %$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given Information

The result of taking $25$ SRSs:

Step 2: Explanation

The red lines under the curve represent the sample means that do not contain the true population proportion.

We note that there are $0$ out of the $25$ samples that do not contain the true proportion and thus $25$ out of the $25$ samples contain the true proportion:

$\frac{25}{25} = 1 = 100 %$

The nearest confidence level is $99 %$ (although $95 %$ could also be a possible used confidence level).

Most popular questions for Math Textbooks

In a poll,

I. Some people refused to answer questions.

II. People without telephones could not be in the sample.

III. Some people never answered the phone in several calls.

Which of these sources is included in the $\pm 2 %$ margin of error announced for the poll?

(a) I only

(b) II only

(c) III only

(d) I, II, and III

(e) None of these

Losing weight A Gallup Poll in November $2008$ found that $59 %$ of the people in its sample said “Yes” when asked, “Would you like to lose weight?” Gallup announced: “For results based on the total sample of national adults, one can say with 95% confidence that the margin of (sampling) error is $\pm 3$ percentage points.”

(a) Explain what the margin of error means in this setting.

(b) State and interpret the $95 %$ confidence interval.

(c) Interpret the confidence level.

You have an SRS of $23$ observations from a Normally distributed population. What critical value would you use to obtain a $98 %$ confidence interval for the mean M of the population if S is unknown?

(a) $2.508$

(b) $2.500$

(c) $2.326$

(d) $2.183$

(e) $2.177$

Reporting cheating What proportion of students are willing to report cheating by other students? A student project put this question to an SRS of $172$ undergraduates at a large university: “You witness two students cheating on a quiz. Do you go to the professor?” Only 19 answered “Yes.” $3$

It's about ME Explain how each of the following would affect the margin of error of a confidence interval, if all other things remained the same.

(a) Increasing the confidence level

(b) Quadrupling the sample size

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