Chapter 8 - Estimating with Confidence

A political candidate is told by his polling organization that a 90% confidence interval for the true proportion of voters who support his candidacy is 0.45 to 0.53. What are the values of the point estimate and margin of error for this interval?

• point estimate = 0.50; margin of error = 0.08.

• point estimate = 0.49; margin of error 0.90.

• point estimate = 0.49; margin of error 0.08.

• point estimate = 0.49; margin of error = 0.04.

• point estimate = 0.49; margin of error cannot be determined without knowing the sample size.

A political candidate is told by his polling organization that a 90% confidence interval for the true proportion of voters who support his candidacy is 0.45 to 0.53. Which of the following claims is justified?

• The majority of registered voters favor this candidate.

• At least 53% of registered voters favor this candidate.

• At least 45% of registered voters favor this candidate.

• Less than 50% of registered voters favor this candidate.

• 90% of registered voters favor this candidate.

A level C confidence interval is

• any interval with margin of error ±C.

• an interval computed from sample data by a method that has probability C of producing an interval containing the true value of the parameter of interest.

• an interval with margin of error ±C that is also correct C% of the time.

• an interval computed from sample data by a method that guarantees that the probability the interval computed captures the parameter of interest is C.

• an interval computed from sample data that has probability (1 – C) of not containing the parameter of interest.

A polling organization announces that the proportion of American voters who favor congressional term limits is 64 percent, with 95% confidence and margin of error of 3 percent. This means that

• 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 percent and 67 percent.

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

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

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

• None of the above are true.

Which of the following sources of error is included in the margin of error?

• chance variation in choosing a random sample

• undercoverage

• some of the subjects did not understand the questions

• voluntary response

• all of the above

A website asks visitors to vote for which of several user-submitted videos is funniest. After a few days, they have collected 250 votes, and they would like to construct a 95% confidence interval for the true proportion of visitors who prefer one of the videos. However, they recognize that their sampling method involves voluntary response, so the data may be biased. How can they compensate for this problem when constructing their confidence interval?

• Use a lower confidence level, such as 80%.

• Use a higher confidence level, such as 99%.

• Collect an additional 250 votes using an SRS.

• Select a smaller sample.

• Throw this data out. There is no way to compensate for this bias.

A traffic consultant wants to estimate the true 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?

• np > 10

• n(1 – p) > 10

• n > 30

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

• The data come from a simple random sample from the population of interest.

The critical value used to construct a confidence interval for a proportion depends upon the

• confidence level being used and the size of the sample.

• size of the sample and the sample proportion.

• confidence level, the size of the sample, and the standard deviation of the population.

• sample size only.

• confidence level only.

A polling organization announces that the proportion of American voters who favor congressional term limits is 64 percent, with a 95% confidence margin of error of 3 percent. If the opinion poll had announced the margin of error for 80% confidence rather than 95% confidence, this margin of error would be

• 3%, because the same sample size is used.

• less than 3%, because we require less confidence.

• less than 3%, because the sample size is smaller.

• greater than 3%, because we require less confidence.

• greater than 3%, because the sample size is smaller.

In a large Midwestern university an SRS of 100 entering freshmen in 2014 showed that 20 finished in the bottom third of their high school class. In 2016, an SRS of 100 entering freshmen showed that 10 finished in the bottom third of their high school class. In both years, the entering freshman class had roughly 6000 students. Which of the following best explains why it was important to know that the university had roughly 6000 entering freshman before using z-procedures in this situation?

• If the size of the freshman classes were much smaller, we could not be confident that the Normality condition for these procedures had been met.

• The central limit theorem would not apply if the population size was below 500.

• We needed to know that the sample sizes were less than 10% of the population size.

• We needed to know that the population sizes were about the same in each year.

• The size of the freshman classes is not important. It is extraneous information.