Estimating a Population Proportion

A survey of 800 women shoppers found that 17% of them shop on impulse. What is the 98% confidence interval for the true proportion of women shoppers who shop on impulse?

• 0.148 < p < 0.192

• 0.136 < p < 0.204

• 0.144 < p < 0.196

• 0.139 < p < 0.201

Answer explanation

The correct confidence interval is 0.139 < p < 0.201 because it captures the true proportion of women shoppers who shop on impulse with 98% confidence.

In a study of 500 people, 60% indicated they prefer online shopping. What is the 90% confidence interval for the true proportion of people preferring online shopping?

• 0.556 < p < 0.644

• 0.560 < p < 0.640

• 0.554 < p < 0.646

• 0.562 < p < 0.638

Answer explanation

The correct confidence interval is 0.556 < p < 0.644 as it captures the true proportion with 90% confidence.

An airline transports over 10,000 passengers daily, and the airline is curious what proportion of their passengers use mobile boarding passes instead of paper passes.  They take a simple random sample of 80 passengers and find that 60 of them use mobile boarding passes.

Based on this sample, which of the following is a 95% confidence interval for the proportion of passengers who use mobile boarding passes?

• (0.625, 0.875)

• (0.637, 0.863)

• (0.655, 0.845)

• (0.670, 0.830)

It was found that in a sample of 90 teenage boys, 70% of them have received speeding tickets. What is the 90% confidence interval of the true proportion of teenage boys who have received speeding tickets?

• (0.621, 0.780)

• (0.591, 0.812)

• (0.584, 0.830)

• (0.615, 0.805)

Estimate the population proportion from the dotplot.

Mathematical Equivalence

ON

Select the correct description

• Average Percent

• Population Proportion

• Sample Proportion

• Percent Slope of a Distribution

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

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

The symbol for the sample proportion is __________.

• Z_c

• p̂

• E

• q

Answer explanation

The symbol for the sample proportion is p̂, which represents the sample proportion in statistics.

A recent study of 750 Internet users in Europe found that 35% of Internet users were women. What is the 95% confidence interval of the true proportion of women in Europe who use the Internet?

• 0.321 < p < 0.379

• 0.316 < p < 0.384

• 0.309 < p < 0.391

• 0.305 < p < 0.395