Estimating Population

A preliminary study suggests that 87% of people agree on an issue. How large must your sample size be so you could be within ± 3% of p calculate at 90% confidence?

• 7

• 466

• 5

• 338

A preliminary study suggests that 17% of people agree on an issue. How large must your sample size be so you could be within ± 5% with 95% confidence?

• 217

• 30

• 2

• 152

A recent survey found that out of 400 random American adults, 89% pay their bills on time. The margin of error in this survey was 2%. What is the interval of values in which the truth is likely found?

• 89% - 91%

• 87% - 89%

• 87% - 91%

• 388 - 402

A research team surveys 200 high schoolers. They find that 57% of them drive to school every day at a 95% confidence level. What is the margin of error?

• 9.0%

• 5.8%

• 6.9%

• 7.0%

Many television viewers express doubts about the validity of certain commercials. In an attempt to answer their critics, Timex Group USA wishes to estimate the proportion of consumers who believe what is shown in Timex television commercials. Let p represent the true proportion of consumers who believe what is shown in Timex television commercials. What is the smallest number of consumers that Timex can survey to guarantee a margin of error of 0.05 of less at a 99% confidence level?

• 550

• 600

• 650

• 700

• 750

What is the critical value z_c for a 99% confidence interval?

• 2.33

• 1.96

• 2.58

• 1.645

Answer explanation

The critical value z_c for a 99% confidence interval is 2.58, which corresponds to the z-score for a 99% confidence level in a standard normal distribution.

For a 95% confidence interval, what is the z-value used in the calculation?

• 1.96

• 2.33

• 1.645

• 2.58

Answer explanation

The correct z-value for a 95% confidence interval is 1.96, which is used in the calculation of the interval.

Tyler wonders what proportion of students at his school would dye their hair blue, if they were allowed to. He surveyed a random sample of 10 students at his school, and 2 of them said they would. Kiran didn’t think Tyler’s estimate was very accurate, so he surveyed a random sample of 100 students, and 17 of them said they would. Whose estimate is more accurate? Explain how you know.

• Tyler's estimate is more accurate.

• Kiran's estimate is more accurate.

Based on Tyler's sample, estimate what proportion of the students would dye their hair blue.

• 0.20

• 0.17

Based on Kiran's sample, estimate what proportion of the students would dye their hair blue.

• 0.20

• 0.17