Proportion Confidence Intervals Requirements

A school administrator is interested in estimating the proportion of students in the district who participate in community service activities. From a random sample of 100 students in the district, the administrator will construct a 99 percent confidence interval for the proportion of all district students who participate in community service activities. Which of the following statements must be true?

• The population proportion will be in the confidence interval.

• The probability that the confidence interval will include the population proportion is 0.99.

• The probability that the confidence interval will include the sample proportion is 0.99.

• The population proportion and the sample proportion will be equal

• The probability that the population proportion and the sample proportion will be equal is 0.99.

A polling agency conducted a survey by selecting 100 random samples, each consisting of 1,200 United States citizens. The citizens in each sample were asked whether they were optimistic about the economy. For each sample, the polling agency created a 95 percent confidence interval for the proportion of all United States citizens who were optimistic about the economy. Which of the following statements is the best interpretation of the 95 percent confidence level?

• With 100 confidence intervals, we can be 95% confident that the sample proportion of citizens of the United States who are optimistic about the economy is correct.

• We would expect about 95 of the 100 confidence intervals to contain the proportion of all citizens of the United States who are optimistic about the economy.

• We would expect about 5 of the 100 confidence intervals to not contain the sample proportion of citizens of the United States who are optimistic about the economy.

• Of the 100 confidence intervals, 95 of the intervals will be identical because they were constructed from samples of the same size of 1,200.

• The probability is 0.95 that 100 confidence intervals will yield the same information about the sample proportion of citizens of the United States who are optimistic about the economy

A commercial for a breakfast cereal is shown during a certain television program. The manufacturer of the cereal wants to estimate the percent of television viewers who watch the program. The manufacturer wants the estimate to have a margin of error of at most 0.02 at a level of 95 percent confidence. Of the following, which is the smallest sample size that will satisfy the manufacturer’s requirements?

• 40

• 50

• 100

• 1700

• 2500

The management team of a company with 10,000 employees is considering installing charging stations for electric cars in the company parking lots. In a random sample of 500 employees, 15 reported owning an electric car. Which of the following is a 99 percent confidence interval for the proportion of all employees at the company who own an electric car?

• 
• 
• 
• 
• 

Sanjay is researching if female students are more or less likely than male students to have received extra credit at a large university. He takes a random sample of 300 students. Sanjay used this sample to build a 95% confidence interval to estimate the difference between the proportion of females and males receiving extra credit. The resulting interval was 0.05±0.07. Based on the interval, what do we know about the corresponding P-value and conclusion at the α=0.05 level of significance?

• The P-value is less than α=0.05, and he cannot conclude that there is a difference between the proportions.

• The P-value is less than α=0.05, and he should conclude that there is a difference between the proportions.

• The P-value is greater than α=0.05, and he cannot conclude that there is a difference between the proportions.

• The P-value is greater than α=0.05, and he should conclude that there is a difference between the proportions.

Sanjay is researching if female students are more or less likely than male students to have received extra credit at a large university. He takes a random sample of 300 students. Sanjay used this sample to build a 95% confidence interval to estimate the difference between the proportion of females and males receiving extra credit. The resulting interval was 0.05±0.07. Based on the interval, what do we know about the corresponding P-value and conclusion at the α=0.05 level of significance?

• The P-value is less than α=0.05, and he cannot conclude that there is a difference between the proportions.

• The P-value is less than α=0.05, and he should conclude that there is a difference between the proportions.

• The P-value is greater than α=0.05, and he cannot conclude that there is a difference between the proportions.

• The P-value is greater than α=0.05, and he should conclude that there is a difference between the proportions.

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

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

A researcher at a major hospital wishes to estimate the proportion of the adult population of the U.S. that has high blood pressure.  How large a sample is needed in order to be 90% confident that the sample proportion will not differ from the true proportion by more than 5%?

• 9

• 271

• 164

• 542

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)