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Chapter 11: Q. 11.70 (page 462)

In this Exercise, we have given the number of successes and the sample size for a simple random sample from a population. In each case,

a. use the one-proportion plus-four z-interval procedure to find the required confidence interval.

b. compare your result with the corresponding confidence interval found in Exercise 11.25-11.30, if finding such a confidence interval was appropriate.

role="math" localid="1651326935007" x=10,n=40,90%level

Short Answer

Expert verified

(a) The one-proportion z-interval technique is adequate because xand n-xare both 5or more.

(b) It is possible to be 90%certain that the confidence interval is between 0.137and 0.363.

Step by step solution

01

Part(a) Step 1: Given Information

The size of a simple random sample from a population, as well as the number of successes.

x=10,n=40,90%level

鈭�n-x=40-10=30, here xand n-x are both 5 or greater.

02

Part(a) Step 2: Explanation

The sample proportion p'=xnis calculated from the data.

1040=0.25

03

Part(b) Step 1: Given Information

The size of a simple random sample from a population, as well as the number of successes.

x=10,n=40,90%level

鈭�n-x=40-10=30, here xand n-x are both 5 or greater.

04

Part(b) Step 2: Explanation

The confidence interval is 95%, which means 伪=0.05.

It is discovered thatza/2=z0.1/2=1.645

The pconfidence interval is of the form

p'-za/2p'1-p'ntop'+za/2p'1-p'n

i.e. 0.25-1.6450.25(1-0.25)40to0.25+1.6450.25(1-0.25)40

i.e. (0.25-0.113)to(0.2+0.124)

i.e.0.137to0.363

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Most popular questions from this chapter

we have given a likely range for the observed value of a sample proportionp^

0.4to0.7

a. Based on the given range, identify the educated guess that should be used for the observed value of p^to calculate the required sample size for a prescribed confidence level and margin of error.

b. Identify the observed values of the sample proportion that will yield a larger margin of error than the one specified if the educated guess is used for the sample-size computation.

Obtain a sample size that will ensure a margin of error of at most the one specified.

Margin of error=0.01

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In this Exercise, we have given the number of successes and the sample size for a simple random sample from a population. In each case,

a. use the one-proportion plus-four z-interval procedure to find the required confidence interval.

b. compare your result with the corresponding confidence interval found in Exercise 11.25-11.30, if finding such a confidence interval was appropriate.

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