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Chapter 10: Q. AP3.3 (page 701)

Sports Illustrated planned to ask a random sample of Division I college athletes, “Do you believe performance-enhancing drugs are a problem in college sports?” Which of the following is the smallest number of athletes that must be interviewed to estimate the true proportion who believe performance-enhancing drugs are a problem within ±2% with 90% confidence?

a.17b.21c.1680d.1702e.2401

Short Answer

Expert verified

The correct optionis

a.n=zα/220.25ME2=1.652×0.250.022≈1702

Step by step solution

01

Given information

We have to find the smallest number of athletes that must be interviewed to estimate the true proportion.

02

Explanation 

Formula sample size:

p^known:n=zα/22p^q^ME2=zα/22p^(1-p^)ME2

p^unknown:n=zα/220.25ME2

the sample size is:

n=zα/220.25ME2=1.652×0.250.022≈1702

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Most popular questions from this chapter

Children make choices Many new products introduced into the market are

targeted toward children. The choice behavior of children with regard to new products is of particular interest to companies that design marketing strategies for these products. As part of one study, randomly selected children in different age groups were compared on their ability to sort new products into the correct product category (milk or juice). Here are some of the data:

Researchers want to know if a greater proportion of 6- to 7-year-olds can sort correctly than 4- to5-year-olds.

a. State appropriate hypotheses for performing a significance test. Be sure to define the parameters of interest.

b. Check if the conditions for performing the test are met.

Men versus women The National Assessment of Educational Progress (NAEP)

Young Adult Literacy Assessment Survey interviewed separate random samples of840

men and 1077women aged 21to 25years.

The mean and standard deviation of scores on the NAEP’s test of quantitative skills were x1=272.40and s1=59.2for the men in the sample. For the women, the results were x ̄2=274.73and s2=57.5.

a. Construct and interpret a 90% confidence interval for the difference in mean score for

male and female young adults.

b. Based only on the interval from part (a), is there convincing evidence of a difference

in mean score for male and female young adults?

School A has 400students and School B has 2700students. A local newspaper wants to compare the distributions of SAT scores for the two schools. Which of the following would be the most useful for making this comparison?

a. Back-to-back stem plots for A and B

b. A scatterplot of A versus B

c. Two dot plots for A and B drawn on the same scale

d. Two relative frequency histograms of A and B drawn on the same scale

e. Two bar graphs for A and B drawn on the same scale

Researchers suspect that Variety A tomato plants have a different average yield than Variety B tomato plants. To find out, researchers randomly select10Variety A and10Variety B tomato plants. Then the researchers divide in half each of10small plots of land in different locations. For each plot, a coin toss determines which half of the plot gets a Variety A plant; a Variety B plant goes in the other half. After harvest, they compare the yield in pounds for the plants at each location. The10differences (Variety A − Variety B) in yield are recorded. A graph of the differences looks roughly symmetric and single-peaked with no outliers. The mean difference is x-A-B=0.343051526=0.200=20%x-A-B=0.34and the standard deviation of the differences is s A-B=0.833051526=0.200=20%=sA-B=0.83.Let μA-B=3051526=0.200=20%μA−B = the true mean difference (Variety A − Variety B) in yield for tomato plants of these two varieties.

A 95% confidence interval forμA-B3051526=0.200=20%μA-Bis given by

a. 0.34±1.96(0.83)3051526=0.200=20%0.34±1.96(0.83)

b.0.34±1.96(0.8310)3051526=0.200=20%0.34±1.96(0.8310)

c. 0.34±1.812(0.8310)3051526=0.200=20%0.34±1.812(0.8310)

d. 0.34±2.262(0.83)3051526=0.200=20%0.34±2.262(0.83)

e.0.34±2.262(0.8310)3051526=0.200=20%0.34±2.262(0.8310)

Two samples or paired data? In each of the following settings, decide whether you should use two-sample t procedures to perform inference about a difference in means or paired t procedures to perform inference about a mean difference. Explain your choice.

a. To test the wear characteristics of two tire brands, A and B, each of 50cars of the same make and model is randomly assigned Brand A tires or Brand B tires.

b. To test the effect of background music on productivity, factory workers are observed. For one month, each subject works without music. For another month, the subject works while listening to music on an MP3 player. The month in which each subject listens to music is determined by a coin toss.

c. How do young adults look back on adolescent romance? Investigators interviewed a random sample of 40couples in their mid-twenties. The female and male partners were interviewed separately. Each was asked about his or her current relationship and also about a romantic relationship that lasted at least 2months when they were aged 15or 16. One response variable was a measure on a numerical scale of how much the attractiveness of the adolescent partner mattered. You want to find out how much men and women differ on this measure.

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