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Chapter 10: Q. 3 (page 667)

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?" How many athletes must be interviewed to estimate the proportion concerned about the use of drugs within 卤2%with 90%confidence?

(a)17(b)21(c)1680(d)1702(e)2401

Short Answer

Expert verified

The number of athletes interviewed is option (d) 1702

Step by step solution

01

Given Information

Given

ME=Margin of error=2%=0.02

c=confidence level=90%=0.90

02

Explanation

Formula sample size

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

p^unknown:n=z伪/220.25ME2

For confidence level 1-伪=0.90, determine z伪/2=z0.05using the normal probability table in the appendix.

z伪/2=1.65

A preliminary estimate p^is unknown, then the sample size is:

localid="1650382239919" n=z伪/220.25ME2=1.652脳0.250.022鈮�1702

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Most popular questions from this chapter

Looking back on love How do young adults look back on adolescent romance? investigators interviewed couples 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 two months when they were aged 15or16 . One response variable was a measure on a numerical scale of how much the attractiveness of the adolescent partner mattered. You want to compare the men and women on this measure.

The elderly fear crime more than younger people, even though they are less likely to be victims of crime. One study recruited separate random samples of 56black women and 63black men over the age of 65from Atlantic City, New Jersey. Of the women, 27said they 鈥渇elt vulnerable鈥� to crime; 46of the men said this.

(a) Construct and interpret a 90%confidence interval for the difference in population proportions (men minus women).

(b) Does your interval from part (a) give convincing evidence of a difference between the population proportions? Explain.

鈥淲ould you marry a person from a lower social class than your own?鈥� Researchers asked this question of a random sample of 385black, never married students at two historically black colleges in the South. Of the 149men in the sample, 91said 鈥淵es.鈥� Among the 236women, 117said 鈥淵es.鈥�14Is there reason to think that different proportions of men and women in this student population would be willing to marry beneath their class?

Holly carried out the significance test shown below to answer this question. Unfortunately, she made some mistakes along the way. Identify as many mistakes as you can, and tell how to correct each one.

State: I want to perform a test of

H0:p1=p2

Ha:p1鈮�p2

at the 95%confidence level.

Plan: If conditions are met, I鈥檒l do a one-sample ztest for comparing two proportions.

  • Random The data came from a random sample of 385 black, never-married students.
  • Normal One student鈥檚 answer to the question should have no relationship to another student鈥檚 answer.
  • Independent The counts of successes and failures in the two groups鈥�91,58,117, and 119鈥�are all at least 10

Do: From the data, p^1=91149=0.61and p^2=117236=0.46.

Test statistic

z=(0.61-0.46)-00.61(0.39)149+0.46(0.54)236=2.91

p=value From Table A, role="math" localid="1650292307192" P(z鈮�2.91)鈮�1-0.3982鈮�0.0018.

Conclude: The p-value, 0.0018, is less than 0.05, so I鈥檒l reject the null hypothesis. This proves that a higher proportion of men than women are willing to marry someone from a social class lower than their own.

Construct and interpret a 95% confidence interval for p1-p2 in Exercise 23. Explain what additional information the confidence interval provides.

A large university is considering the establishment of a schoolwide recycling program. To gauge interest in the program by means of a questionnaire, the university takes separate random samples of undergraduate students, graduate students, faculty, and staff. This is an example of what type of sampling design?

(a) Simple random sample

(b) Stratified random sample

(c) Convenience sample

(d) Cluster sample

(e) Systematic sample

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