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Chapter 11: Q. 11.74 (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=3,n=100,99%level

Short Answer

Expert verified

(a) The one-proportion z-interval technique is appropriate since role="math" localid="1651401865385" xis not larger than 5and n-x>5is not greater than 5or greater.

(b) It is possible to be 99%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=3andn=100,99%level

鈭�n-x=100-3=97, here xand n-x are both 5 or greater.

02

Part(a) Step 2: Explanation

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

3100=0.03

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=3andn=100,99%level

鈭�n-x=100-3=97, here xand n-x are both 5 or greater.

04

Part(b) Step 2: Explanation

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

It is discovered thatza/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

11.91 Economic Stimulus. In a national poll, 1053 U.S. adults were asked, "As you may know, Congress is considering a new economic stimulus package of at least 800 billion dollars. Do you favor or oppose Congress passing this legislation?" Of those sampled, 548 favored passage.
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