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Chapter 11: Q. 11.72 (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 Exercises 11.25-11.30, if finding such a confidence interval was appropriate.

x=40,n=50,95%level

Short Answer

Expert verified

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

(b) The confidence interval can be estimated to be between 0.689and 0.911with a 95%confidence level.

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=40andn=50,95%level

role="math" localid="1651400180077" 鈭�n-x=50-40=10, here xand n-xare both 5or greater.

02

Part(a) Step 2: Explanation

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

4050=0.8

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=40andn=50,95%level

鈭�n-x=50-40=10, 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=z0.05/2=1.96

The pconfidence interval is of the form

p'-z伪/2p'1-p'ntop'+z伪/2p'1-p'n

i.e. 0.8-1.9600.8(1-0.8)50to0.8-1.9600.8(1-0.8)50

i.e. (0.8-0.111)to(0.8+0.111)

i.e.0.689to0.911

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Most popular questions from this chapter

Body Mass Index. Refer to Exercise 11.111 and find and interpret a 90% confidence interval for the difference between the percentages of adults in the Iwo degree categories who have an above healthy weight.

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

Margin of error=0.01

Confidence level=90%

a. Determine the sample proportion.

b. Decide whether using the one-proportion z-test is appropriate.

c. If appropriate, use the one-proportion z-test to perform the specified hypothesis test.

x=35

n=50

H0:p=0.6

role="math" localid="1651304589496" Ha:p>0.6

伪=0.05

Obtain a sample size

Margin of error =0.01

Confidence level =95%

likely range=0.2-0.4

Suppose that you are using independent samples to compare two population proportions.

Fill in the blanks.

a. The mean of all possible differences between the two sample proportions equals the

b. For large samples, the possible differences between the two sample proportions have approximately a distribution.
See all solutions

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