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Chapter 8: Q.29 (page 496)

AIDS and risk factors In the National AIDS

Behavioral Surveys sample of 2673adult heterosexuals, 0.2%had both received a blood transfusion and had a sexual partner from a group at high risk of A I D S. We want to estimate the proportion pin the population who share these two risk factors.

Short Answer

Expert verified

All three conditions for confidence level is not satisfied.

Step by step solution

01

Step-1 Given Information

Given in the question that,

Population size 2673

Number of success 0.2%of population size. We want to estimate the proportion pin the population who share these two risk factors.

02

Step-2 Explanation

Three conditions must be met in order to construct a confidence interval. Random, Independent, and Normal are the conditions.

The randomness requirement is not met since all of the samples taken are related to one another.

The requirement for independence is satisfied because the sample size is less than 10%of the population size.

The survey findings show that the number of successes is fewer than 10, indicating that the typical condition is not met.

As a result, none of the three confidence interval conditions are met.

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Most popular questions from this chapter

Trace metals found in wells affect the taste of drinking water, and high concentrations can pose a health risk. Researchers measured the concentration of zinc (in milligrams/liter) near the top and the bottom of 10randomly selected wells in a large region. The data are provided in the table below.

(a) Construct and interpret a 95%confidence interval for the mean difference μin the zinc concentrations from these two locations in the wells.

(b) Does your interval in part (a) give convincing evidence of a difference in zinc concentrations at the top and bottom of wells in the region? Justify your answer.

Alcohol abuse has been described by college presidents as the number one problem on campus, and it is an important cause of death in young adults. How common is it? A survey of 10,904 randomly selected U.S. college students collected information on drinking behavior and alcohol-related problems." The researchers defined "frequent binge drinking" as having five or more drinks in row three or more times in the past two weeks. According to this definition, 2486 students were classified as frequent binge drinkers.

1. Identify the population and the parameter of interest.

2. Check conditions for constructing a confidence interval for the parameter.

3. Find the critical value for a 99 \% confidence interval. Show your method. Then calculate the interval.

4. Interpret the interval in context.

An online poll posed the following question:

It is now possible for school students to log on to Internet sites and download homework. Everything from book reports to doctoral dissertations can be downloaded free or for a fee. Do you believe that giving a student who is caught plagiarizing an F for their assignment is the right punishment?

Of the 20,125people who responded, 14,793clicked “Yes.” That’s 73.5%of the sample. Based on this sample, a 95%confidence interval for the percent of the population who would say “Yes” is 73.5% ±0.61. Which of the three inference conditions is violated? Why is this confidence interval worthless?

A radio talk show host with a large audience is interested in the proportion pof adults in his listening area who think the drinking age should be lowered to eighteen. To find this out, he poses the following question to his listeners: "Do you think that the drinking age should be reduced to eighteen in light of the fact that eighteen-year-olds are eligible for military service?" He asks listeners to phone in and vote "Yes" if they agree the drinking age should be lowered and "No" if not. Of the 100people who phoned in, 70answered "Yes." Which of the following conditions for inference about a proportion using a confidence interval are violated?

I. The data are a random sample from the population of interest.

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(a) I only

(c) III only

(c) I, II, and III

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