Proportion Interval Test

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

As part of a national sleep study, a random sample of adults was selected and surveyed about their physical activity and the number of hours they sleep each night. Of the 183 adults who exercised regularly (exercisers), 59 percent reported sleeping at least seven hours at night. Of the 88 adults who did not exercise regularly (nonexercisers), 52 percent reported sleeping at least seven hours at night. Which of the following is the most appropriate standard error for a confidence interval for the difference in proportions of adults who sleep at least seven hours at night among exercisers and nonexercisers?

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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

On the day before an election in a large city, each person in a random sample of 1,000 likely voters is asked which candidate he or she plans to vote for. Of the people in the sample, 55 percent say they will vote for candidate Taylor. A margin of error of 3 percentage points is calculated. Which of the following statements is appropriate?

• The proportion of all likely voters who plan to vote for candidate Taylor must be the same as the proportion of voters in the sample who plan to vote for candidate Taylor (55 percent), because the data were collected from a random sample.

• The sample proportion minus the margin of error is greater than 0.50, which provides evidence that more than half of all likely voters plan to vote for candidate Taylor.

• It is not possible to draw any conclusion about the proportion of all likely voters who plan to vote for candidate Taylor because the 1,000 likely voters in the sample represent only a small fraction of all likely voters in a large city.

• It is not possible to draw any conclusion about the proportion of all likely voters who plan to vote for candidate Taylor because this is not an experiment.

• It is not possible to draw any conclusion about the proportion of all likely voters who plan to vote for candidate Taylor because this is a random sample and not a census.

A national health study reported that the proportion of students with elevated blood pressure is 0.15. The principal of a local high school believes that the proportion of students in the school with elevated blood pressure is greater than 0.15. If a large random sample is used, which of the following is the most appropriate test to investigate the principal’s belief?

• A z-test for a proportion

• A z-test for a difference between two proportions

• A chi-square test for homogeneity of proportions

• A t-test for a mean

• A matched-pairs t-test

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 study found that in a sample of 44 subjects, 9 of agree that children under 6 shouldn’t be taken to nice restaurants. The 95% confidence interval for p is (0.082, 0.318). Interpret this interval.

• 95% of the time the proportion of people who believe children under 6 shouldn't be taken to nice restaurants will be between 8.2% and 31.8%.

• The population proportion of people who believe children under 6 shouldn't be taken to nice restaurants is between 8.2% and 31.8%.

• The probability that the proportion of people who believe children under 6 shouldn't be taken to nice restaurants will be between 8.2% and 31.8% is 95%.

• Based on this sample, I am 95% confident that the proportion of people who believe children under 6 shouldn't be taken to nice restaurants is between 8.2% and 31.8%.

Which confidence would result in a wider interval (assuming nothing else changed), 91% or 97%?

• 97%, z* is larger for higher confidence intervals

• 97%, the standard error is larger for higher confidence intervals

• 91%, z* is larger for lower confidence intervals

• 91%, the standard error is smaller for lower confidence intervals

Which of the following is an example of an interval estimate?

• point estimate 

• critical value

• confidence interval

• statistic

Tina wants to know if the proportion of people who buy burgers is at all affected by her open mic reading. If p=0.8 before her reading, what is an appropriate set of hypotheses?

• Ho: p = 0.8
  Ha: p > 0.8

• Ho: p = 0.8
  Ha: p < 0.8

• Ho: p ≠ 0.8
  Ha: p = 0.8

• Ho: p= 0.8
  Ha: p ≠ 0.8