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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 渭in 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.

A telephone poll of an SRS of 1234 adults found that 62% are generally satisfied with their lives. The announced margin of error for the poll was 3%. Does the margin of

error account for the fact that some adults do not have telephones?

(a) Yes. The margin of error includes all sources of error in the poll.

(b) Yes. Taking an SRS eliminates any possible bias in estimating the population proportion.

(c) Yes. The margin of error includes under coverage but not nonresponse.

(d) No. The margin of error includes nonresponse but is not under coverage.

(e) No. The margin of error only includes sampling variability.

R8.5. Smart kids A school counselor wants to know how smart the students in her school are. She gets funding from the principal to give an IQ test to an SRS of 60of the over 1000students in the school. The mean IQ score was 114.98and the standard deviation was 14.80.
(a) Describe the parameter 渭 in this setting.
(b) Explain why the Normal condition is met in this case.
(c) Construct a 90% confidence interval for the mean IQ score of students at the school.
(d) Interpret your result from part (c) in context.

56. The SAT again High school students who take the SAT Math exam a second time generally score higher than on their first try. Past data suggest that the score increase has a standard deviation of about 50 points.
How large a sample of high school students would be needed to estimate the mean change in SAT score to within 2 points with 95% confidence? Show your work.

Good wood? A lab supply company sells pieces of Douglas fir 4inches long and 1.5inches square for force experiments in science classes. From experience, the strength of these pieces of wood follows a Normal distribution with standard deviation 3000pounds. You want to estimate the mean load needed to pull apart these pieces of wood to within 1000pounds with 95%confidence. How large a sample is needed? Show your work.

- Understand how the margin of error of a confidence interval changes with the sample size and the level of confidence C.
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