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Chapter 11: Q.11.19 (page 459)

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

0.2to0.4

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.

Short Answer

Expert verified

(a)The sample proportion is estimated to be 0.2.

(b)The observed values of the sample proportion is0.2<p^<0.4

Step by step solution

01

Part (a) Step 1: Given Information 

Given in the question that, the confidence interval is0.2-0.4we have to 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.

02

Part (a) Step 2: Explanation 

The educated prediction is the value that is closest to the midpoint of the expected range of 0.2-0.4dollars. As a result, 0.2is the educated estimation for the sample proportion.

03

Part (b) Step 1: Given Information 

Given in the question that, the confidence interval is0.2-0.4we have to

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.

04

Part (b) Step 2: Explanation 

A bigger margin of error is provided by the value range of 0.2-0.4. As a result, the observed sample proportion values vary from 0.2-0.4. That is,0.2<p^<0.4.

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Most popular questions from this chapter

Literate Adults. Suppose that you have been hired to estimate the percentage of adults in your state who are literate. You take a random sample of 100adults and find that 96are literate. You then obtain a 95%confidence interval of

0.96卤1.96路(0.96)(0.04)/100

or 0.922to 0.998. From it you conclude that you can be 95%confident that the percentage of all adults in your state who are literate is somewhere between 92.2%and 99.8%. Is anything wrong with this reasoning?

Obtain a sample size

Margin of error =0.01

Confidence level =95%

likely range=0.2-0.4

x1=18,n1=30,x2=10,n2=20;95%confidence interval

Folic Acid and Birth Defects. For several years, evidence had been mounting that folic acid reduces major birth defects. A. Creizel and I. Dudas of the National Institute of Hygiene in Budapest directed a study that provided the strongest evidence to date. Their results were published in the paper "Prevention of the First Occurrence of Neural-Tube Defects by Periconceptional Vitamin Supplementation" (New England Journal of Medicine, Vol. 327(26). p. 1832 ). For the study, the doctors enrolled women prior to conception and divided them randomly into two groups. One group, consisting of 2701 women, took daily multivitamins containing 0.8mg of folic acid; the other group, consisting of 2052 women, received nay A. Creizel and L. Duxlas of the National Institute of Hygiene i) Budapest directed a study that provided the strongest evidence to date Their results were published in the paper "Prevention of the Firs Occurrence of Neural-Tube Defects by Periconceptional Vitamin Supplementation" (New England Journal of Medicine, Vol. 327(26). p. 1832 ). For the study, the doctors enrolled women prior to conception and divided them randomly into two groups. One group, consisting of 2701 women, took daily multivitamins containing 0.8mg of folic acid; the other group. consisting of 2052 women, received only trace elements. Major birth defects occurred in 35 cases when the women took folic acid and in 47 cases when the women did not.

a. At the 1%significance level, do the data provide sufficient evidence to conclude that women who take folic acid are at lesser risk of having children with major birth defects?

b. Is this study a designed experiment or an observational study? Explain your answer.

c. In view of your answers to parts (a) and (b), could you reasonably conclude that taking folic acid causes a reduction in major birth defects? Explain your answer.

Refer to the study on ordering vegetarian considered in Examples 11.8-11.10.

a. Without making a guess for the observed values of the sample proportions, find the common sample size that will ensure a margin of error of at most 0.01for a 90%confidence interval. Hint: Use Exercise 11.133.

b. Find a90%confidence interval for p1-p2if, for samples of the size determined in part (a), 38.3%of the men and 43.7%of the women sometimes order veg.

c. Determine the margin of error for the estimate in part (b), and compare it to the required margin of error specified in part (a).
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