AP STATS Chapter 8 Review

The government claims that students earn a mean of $4500 during their summer break from studies. A random sample of students gave a sample average of $3975, and a 95% confidence interval was found to be $3525 < μ < $4425. Which of the following is a correct interpretation of 95% confidence?

• if the study were to be repeated many times, there is a 95% probability that the true average summer earnings is not $4500 as the government claims.

• because our specific confidence interval does not contain the value $4500 there is a 95% probability that the true average summer earnings is not $4500.

• if we were to repeat our survey many times, then about 95% of all the confidence intervals will contain the value $4500.

• if we repeat our survey many times, then about 95% of our confidence intervals will contain the true value of the average earnings of students.

• there is a 95% probability that the true average earnings are between $3525 and $4425 for all students.

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CCSS.HSS.IC.B.4

You want to estimate the mean SAT score for a population of students with a 90% confidence interval. Assume that the population standard deviation is σ = 100. If you want the margin of error to be no more than 10, you will need a minimum sample size of approximately

• 17

• 38

• 271

• 385

• 1646

An SRS of 50 students at a large middle school are asked, “Do you have a television in your bedroom? Twenty-eight of the students responded “yes.” If ˆp = the proportion of students who answered “yes,” what is the standard error of pˆ ?

• 0.005

• 0.010

• 0.070

• 0.106

• The standard error cannot be calculated unless we know the standard deviation.

The college newspaper of a large Midwestern university periodically conducts a survey of students on campus to determine the attitude on campus concerning issues of interest. Pictures of the students interviewed along with quotes of their responses are printed in the paper. Students are interviewed by a reporter “roaming” the campus selecting students to interview “haphazardly.” On a particular day the reporter interviews five students and asks them if they feel there is adequate student parking on campus. Four of the students say, “no.” Which of the following conditions for inference about a proportion using a confidence interval are violated in this example?

I. The data are an SRS from the population of interest.

II. The population is at least ten times as large as the sample.

III. npˆ ≥ 10 and n(1− pˆ) ≥10 .

• I only

• II only

• III only

• I and III

• All three conditions are violated.

For sample sizes of at least 30, the t-confidence interval for a population mean is robust with respect to which of the following concerns?

• Undercoverage.

• Lack of randomness in sampling.

• Skew in the population distribution.

• The presence of extreme outliers.

• None of the other choices.

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CCSS.HSS.IC.B.4

A letter home to the parents of seniors at Westgate High School says, “a simple random sample of 30 Westgate seniors that took the SAT-M test this year produced a mean of 512 and a standard deviation of 95. A confidence interval for the true mean for all WHS seniors is 512.00 ± 47.8.” The confidence level for this interval is

• 90%

• 95%

• 99%

• 99.5%

• over 99.9%

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CCSS.HSS.IC.B.4

In an opinion poll, 25% of a random sample of 200 people said that they were strongly opposed to having a state lottery. The standard error of the sample proportion is approximately

• 0.0094

• 0.0306

• 0.0353

• 0.2500

• 6.1237

A traffic consultant wants to estimate the proportion of cars on a certain street that have more than two occupants. She stands at the side of the road for two hours on a weekday afternoon and flips a coin each time a car approaches. If the coin comes up heads, she counts the number of occupants in the car. After two hours, she has counted 103 cars, 15 of which had more than two occupants. Which condition for constructing a confidence interval for a proportion has she failed to satisfy?

• n ≥ 30

• np ≥10

• n(1− p) ≥10

• The sample is less than 10% of the population.

• The data is an SRS from the population of interest.

A polling organization announces that the proportion of American voters who favor congressional term limits is 64%, with a 95% confidence margin of error of 3%. Which of the following statements is a correct interpretation of 95% confidence?

• If the poll were conducted again in the same way, there is a 95% chance that the fraction of voters favoring term limits in the second poll would be between 61% and 67%.

• There is a 95% probability that the true percent of voters favoring term limits is between 61% and 67%

• If the poll were conducted again the same way, there is a 95% probability that the percent of voters favoring term limits in the second poll would be within 3% of the percent favoring term limits in the first poll.

• Among 95% of the voters, between 61% and 67% favor term limits.

• None of the others

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CCSS.HSS.IC.B.4

Some scientists believe that a new drug would benefit about half of all people with a certain blood disorder. To estimate the proportion of patients who would benefit from taking the drug, the scientists will administer it to a random sample of patients who have the blood disorder. What sample size is needed so that the 95% confidence interval will have a margin of error of no more than 3%?

• 748

• 1068

• 1503

• 2056

• 2401

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CCSS.HSS.IC.B.4