Introduction to Statistics and Data Analysis
Introduction to Statistics and Data Analysis
5th Edition
ISBN: 9781305750999
Author: Peck Olson Devore
Publisher: CENGAGE C
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Chapter 9.2, Problem 12E

a.

To determine

Check whether the sample size is large enough to use the confidence interval for the given combinations of n and p^.

a.

Expert Solution
Check Mark

Answer to Problem 12E

Yes, the sample size of 50 is large enough for the interval to be appropriate.

Explanation of Solution

Calculation:

The given information is that n=50 and p^=0.30.

The interval is appropriate, if np^10 and n(1p^)10.

Verify the conditions:

Substitute, n=50 and p^=0.30 in the above conditions.

np^=50(0.3)=1510

n(1p^)=50(10.3)=50(0.7)=3510

Thus, both the conditions are satisfied.

The sample size of 50 is large enough for the interval to be appropriate.

b.

To determine

Explain whether the sample size is large enough to use the confidence interval for the given combinations of n and p^.

b.

Expert Solution
Check Mark

Answer to Problem 12E

No, the sample size of 50 is not large enough for the interval to be appropriate.

Explanation of Solution

Calculation:

The given information is that n=50 and p^=0.05.

Verify the conditions:

Substitute, n=50 and p^=0.05 in the conditions specified in Part (a).

np^=50(0.05)=2.5<10

n(1p^)=50(10.05)=50(0.95)=47.510

Thus, the first condition is not satisfied.

The sample size of 50 is not large enough for the interval to be appropriate.

c.

To determine

Define whether the sample size is large enough to use the confidence interval for the given combinations of n and p^.

c.

Expert Solution
Check Mark

Answer to Problem 12E

No, the sample size of 15 is not large enough for the interval to be appropriate.

Explanation of Solution

Calculation:

The given information is that n=15 and p^=0.45.

Verify the conditions:

Substitute, n=15 and p^=0.45 in the conditions specified in Part (a).

np^=15(0.45)=6.75<10

n(1p^)=15(10.45)=50(0.55)=8.25<10

Thus, the both the conditions are not satisfied.

The sample size of 15 is not large enough for the interval to be appropriate.

d.

To determine

Elucidate whether the sample size is large enough to use the confidence interval for the given combinations of n and p^.

d.

Expert Solution
Check Mark

Answer to Problem 12E

No, the sample size of 100 is not large enough for the interval to be appropriate.

Explanation of Solution

Calculation:

The given information is that n=100 and p^=0.01.

Verify the conditions:

Substitute n=100 and p^=0.01 in the conditions specified in Part (a).

np^=100(0.01)=1<10

n(1p^)=100(10.01)=100(0.99)=9910

Thus, the first condition is not satisfied.

The sample size of 100 is not large enough for the interval to be appropriate.

e.

To determine

Examine whether the sample size is large enough to use the confidence interval for the given combinations of n and p^.

e.

Expert Solution
Check Mark

Answer to Problem 12E

Yes, the sample size of 100 is large enough for the interval to be appropriate.

Explanation of Solution

Calculation:

The given information is that n=100 and p^=0.70.

Verify the conditions:

Substitute, n=100 and p^=0.70 in the conditions specified in Part (a).

np^=100(0.70)=7010

n(1p^)=100(10.70)=100(0.30)=3010

Thus, both the conditions are satisfied.

The sample size of 100 is large enough for the interval to be appropriate.

f.

To determine

Describe whether the sample size is large enough to use the confidence interval for the given combinations of n and p^.

f.

Expert Solution
Check Mark

Answer to Problem 12E

Yes, the sample size of 40 is large enough for the interval to be appropriate.

Explanation of Solution

Calculation:

The given information is that n=40 and p^=0.25.

Verify the conditions:

Substitute, n=40 and p^=0.25 in the conditions specified in Part (a).

np^=40(0.25)=1010

n(1p^)=40(10.25)=40(0.75)=3010

Thus, both the conditions are satisfied.

The sample size of 40 is large enough for the interval to be appropriate.

g.

To determine

Justify whether the sample size is large enough to use the confidence interval for the given combinations of n and p^.

g.

Expert Solution
Check Mark

Answer to Problem 12E

Yes, the sample size of 60 is large enough for the interval to be appropriate.

Explanation of Solution

Calculation:

The given information is that n=60 and p^=0.25.

Verify the conditions:

Substitute, n=60 and p^=0.25 in the conditions specifies in Part (a).

np^=60(0.25)=1510

n(1p^)=60(10.25)=60(0.75)=4510

Thus, both the conditions are satisfied.

The sample size of 60 is large enough for the interval to be appropriate.

h.

To determine

Check whether the sample size is large enough to use the confidence interval for the given combinations of n and p^.

h.

Expert Solution
Check Mark

Answer to Problem 12E

No, the sample size of 80 is not large enough for the interval to be appropriate.

Explanation of Solution

Calculation:

The given information is that n=80 and p^=0.1.

Verify the conditions:

Substitute, n=80 and p^=0.1 in the conditions specifies in Part (a).

np^=80(0.1)=8<10

n(1p^)=80(10.1)=80(0.90)=7210

Thus, the first condition is not satisfied.

The sample size of 80 is not large enough for the interval to be appropriate.

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Chapter 9 Solutions

Introduction to Statistics and Data Analysis

Ch. 9.2 - The formula used to calculate a large-sample...Ch. 9.2 - Prob. 12ECh. 9.2 - Discuss how each of the following factors affects...Ch. 9.2 - Prob. 14ECh. 9.2 - Based on data from a survey of 1200 randomly...Ch. 9.2 - Prob. 16ECh. 9.2 - If a hurricane was headed your way, would you...Ch. 9.2 - Prob. 18ECh. 9.2 - Prob. 19ECh. 9.2 - Prob. 20ECh. 9.2 - Prob. 21ECh. 9.2 - Prob. 22ECh. 9.2 - Prob. 23ECh. 9.2 - Prob. 24ECh. 9.2 - Prob. 25ECh. 9.2 - Prob. 26ECh. 9.2 - Prob. 27ECh. 9.2 - The Gallup Organization conducts an annual survey...Ch. 9.2 - The article Hospitals Dispute Medtronic Data on...Ch. 9.2 - Prob. 30ECh. 9.2 - A discussion of digital ethics appears in the...Ch. 9.2 - In spite of the potential safety hazards, some...Ch. 9.2 - Prob. 33ECh. 9.3 - Given a variable that has at distribution with the...Ch. 9.3 - The formula used to calculate a confidence...Ch. 9.3 - USA TODAY reported that the average amount of...Ch. 9.3 - Samples of two different models of cars were...Ch. 9.3 - Prob. 38ECh. 9.3 - In a study of academic procrastination, the...Ch. 9.3 - Medical research has shown that repeated wrist...Ch. 9.3 - Prob. 41ECh. 9.3 - Prob. 42ECh. 9.3 - Suppose that a random sample of 50 bottles of a...Ch. 9.3 - Prob. 44ECh. 9.3 - The article The Association Between Television...Ch. 9.3 - Prob. 46ECh. 9.3 - Because of safety considerations, in May 2003 the...Ch. 9.3 - Example 9.3 gave the following airborne times (in...Ch. 9.3 - Prob. 49ECh. 9.3 - Five students visiting the student health center...Ch. 9.3 - The Bureau of Alcohol, Tobacco, and Firearms...Ch. 9.3 - The formula described in this section for...Ch. 9.4 - The following quote is from the article Credit...Ch. 9.4 - Authors of the news release titled Major Gaps...Ch. 9.4 - The paper The Curious Promiscuity of Queen Honey...Ch. 9 - Prob. 56CRCh. 9 - Prob. 57CRCh. 9 - Prob. 58CRCh. 9 - Prob. 59CRCh. 9 - Prob. 60CRCh. 9 - Prob. 61CRCh. 9 - A manufacturer of small appliances purchases...Ch. 9 - Prob. 63CRCh. 9 - A manufacturer of college textbooks is interested...Ch. 9 - Prob. 65CRCh. 9 - The confidence intervals presented in this chapter...Ch. 9 - Prob. 67CRCh. 9 - The interval from 2.33 to 1.75 captures an area of...Ch. 9 - Prob. 69CR
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