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Chapter 11: Q.8 (page 480)

Smallpox Vaccine. ABCNEWS.com published the results of a poll that asked U.S. adults whether they would get a smallpox shot if it were available. Sampling, data collection, and tabulation were done by TNS Intersearch of Horsham, Pennsylvania. When the risk of the vaccine was described in detail, 4 in 10 of those surveyed said they would take the smallpox shot. According to the article, "the results have a three-point margin of error" (for a 0.95 confidence level). Use the information provided to obtain a 95% confidence interval for the percentage of all U.S. adults who would take a smallpox shot, knowing the risk of the vaccine.

Short Answer

Expert verified

The confidence interval for the percentage of all adults who would take a smallpox vaccination may be 95%confidence, indicating a risk of 0.37to 0.43for the vaccine.

Step by step solution

01

Given Information

p=percentage of all adults who would take a smallpox shot indicates the risk of the vaccine.

Here x=4

and n=10.

02

Explanation

The confidence interval for p:

p^±zα/2p^(1-p^)n

Where

zα/2p^(1-p^)n=Margin of error

p^=xn

=410

=0.40

The confidence interval for p:

=p^±zα/2p^(1-p^)n

=0.40±0.03[margin of error is given as3-point]i.e,0.37and0.43

i.e,37%and43%

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Most popular questions from this chapter

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).

11.92 Delayed Perinatal Stroke. In the article "Prothrombotic Factors in Children With Stroke or Porencephaly" (Pediatrics Journal, Vol. 116, Issue 2, pp. 447-453), J. Lynch et al. compared differences and similarities in children with arterial ischemic stroke and porencephaly. Three classification categories were used: perinatal stroke, delayed perinatal stroke, and childhood stroke. Of 59children, 25were diagnosed with delayed perinatal stroke. At the 5%significance level, do the data provide sufficient evidence to conclude that delayed perinatal stroke does not comprise one-third of the cases among the three categories?

Why is statistical inference generally used to obtain information about a population proportion?

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

a. Obtain the margin of error for the estimate of the difference between the proportions of men and women who sometimes order veg by taking half the length of the confidence interval found in Example 11.10on page 473. Interpret your answer in words.

b. Obtain the margin of error for the estimate of the difference between the proportions of men and women who sometimes order veg by applying Exercise 11.132.

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="1651327118166" x=35,n=50,99%level
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