Estimating a Population Proportion

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 or less at a 99.7% confident level?

• Impossible to calculate

• 100

• 882

• 883

• 900

Alma is estimating the proportion of students in her school district who, in the past month, read at least 1 book. From a random sample of 50 students, she found that 32 students read at least 1 book last month. Assuming all conditions for inference are met, which of the following defines a 90 percent confidence interval for the proportion of all students in her district who read at least 1 book last month?

A town council wants to estimate the proportion of residents who are in favor of a proposal to upgrade the computers in the town library. A random sample of 100 residents was selected, and 97 of those selected indicated that they were in favor of the proposal. Is it appropriate to assume that the sampling distribution of the sample proportion is approximately normal?

• No, because the sample is not large enough to satisfy the normality conditions.

• No, because the size of the population is not known.

• Yes, because the sample was selected at random.

• Yes, because sampling distributions of proportions are modeled with a normal model.

• Yes, because the sample is large enough to satisfy the normality conditions.

Sue and Javier are working on a statistics project to estimate the proportion of students at their school who have a pet dog. Sue selects a random sample of 81 students from the 2,400 students at their school, and Javier selects a separate random sample of 64 students. They will both construct a 90 percent confidence interval from their estimates. Consider the situation in which the sample proportion from Sue’s sample is equal to the sample proportion from Javier’s sample. Which of the following statements correctly describes their intervals?

• Javier's interval will have a greater degree of confidence than Sue's interval will.

• Sue's interval will have a greater degree of confidence than Javier's interval will.

• The width of Sue's interval will be the same as the width of Javier's interval.

• The width of Sue's interval will be wider than the width of Javier's interval.

• The width of Sue's interval will be narrower than the width of Javier's interval.

Suppose a 90 percent confidence interval to estimate a population proportion was calculated from a sample proportion of 18 percent and a margin of error of 4 percent. What is the width of the confidence interval?

• 2 percent

• 4 percent

• 8 percent

• 16 percent

• 36 percent

Suppose a researcher wants to use a confidence interval to estimate an unknown population proportion p. Which of the following is not a correct statement?

• The endpoints of the interval can vary with each new sample.

• The probability that p is in the interval is equal to the level of confidence for the interval.

• Whether the interval captures p is not known with certainty.

• The population proportion p is fixed (constant), but the sample proportion p-hat can vary from sample to sample.

• The interval either does or does not capture p.

A 90% confidence interval for the proportion different p1-p2 was calculated to be (0.247, 0.325). Which of the following conclusions is supported by the interval?

• There is evidence to conclude that p1>p2 because 0.325 is greater than 0.247.

• There is evidence to conclude that p1<p2 because 0.325 is greater than 0.247.

• There is evidence to conclude that p1>p2 because all values in the interval are positive.

• There is evidence to conclude that p1<p2 because all values in the interval are positive.

• There is evidence to conclude that p2>p1 because 0.247 and 0.325 are both greater than 0.05.

Which condition, if met, says the sampling distribution of p-hat will be approximately normal?

• Random Sample

• 10% Condition

• Large Counts condition

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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