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Chapter 11: Q. 11.73 (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=16,n=20,90%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=16andn=20,90%level

鈭�n-x=20-16=4, here xand n-x are both 5 or greater.

02

Part(a) Step 2: Explanation

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

1620=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=16andn=20,90%level

鈭�n-x=20-16=4, 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 that role="math" localid="1651401333333" za/2=z0.1/2=1.645

The pconfidence interval is of the form

p'-z伪/2p'1-p'ntop'+z伪/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

Buckling Up. The National Highway Traffic Safety Administration collects data on seat-belt use and publishes results in the document Occupant Restraint Use. Of 1000 drivers 16-24 years old, 79% said that they buckle up, whereas 924 of 1100 drivers 25-69 years old said that they did. At the 1%significance level, do the data provide sufficient evidence to conclude that there is a difference in seat-belt use between the two age groups?

11.98 Consider a hypothesis test for two population proportions with the null hypothesis H0:p1=p2. What parameter is being estimated by the
a. sample proportion p1?
b. sample proportion p^2 ?
c. pooled sample proportion p^p ?

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=40

n=50

H0:p=0.6

Ha:p>0.6

伪=0.01

We have given a likely range for the observed value of a sample proportion p^

0.7orless

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.

Racial Crossover. In the paper "The Racial Crossover in Comorbidity, Disability, and Mortality" (Demography, Vol. 37(3), pp. 267-283), N. Johnson investigated the health of independent random samples of white and African-American elderly (aged 70 years or older). Of the 4989 white elderly surveyed, 529 had at least one stroke, whereas 103 of the 906 African-American elderly surveyed - Lported at least one stroke. At the 5%significance level, do the data suggest that there is a difference in stroke incidence between white and African-American elderly?
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