Senate Filibuster You wish to estimate, with 99% confidence, the population proportion of U.S. adults who disapprove of the U.S Senate’s use of the filibuster. Your estimate must be accurate within 2% of the population proportion.
b. Find the minimum sample size needed, using a prior survey that found that 34% of U.S. adults disapprove of the U.S Senate’s use of the filibuster. (Source: Monmouth University)

In Exercises 19–22, let p be the population proportion for the situation. (a) Find point estimates of p and q, (b) construct 90% and 95% confidence intervals for p, and (c) interpret the results of part (b) and compare the widths of the confidence intervals.

In a survey of 73,901 college graduates, 23,991 obtained a postgraduate degree. (Adapted from Gallup)

You wish to estimate, with 95% confidence, the population proportion of U.S. adults who have taken or planned to take a winter vacation in a recent year. Your estimate must be accurate within 5% of the population proportion.

a. No preliminary estimate is available. Find the minimum sample size needed.

In a survey of 2096 U.S. adults, 1740 think football teams of all levels should require players who suffer a head injury to take a set amount of time off from playing to recover. (Adapted from The Harris Poll)

a. Find the point estimate for the population proportion.

In a survey of 2096 U.S. adults, 1740 think football teams of all levels should require players who suffer a head injury to take a set amount of time off from playing to recover. (Adapted from The Harris Poll)

b. Construct a 95% confidence interval for the population proportion. Interpret the results.

Fast Food You wish to estimate, with 90% confidence, the population proportion of U.S. families who eat fast food at least once per week. Your estimate must be accurate within 3% of the population proportion.

a. No preliminary estimate is available. Find the minimum sample size needed.

Fast Food You wish to estimate, with 90% confidence, the population proportion of U.S. families who eat fast food at least once per week. Your estimate must be accurate within 3% of the population proportion.

b. Find the minimum sample size needed, using a prior study that found that 83% of U.S. families eat fast food at least once per week. (Source: The Barbecue Lab)

Constructing Confidence Intervals In Exercises 25 and 26, use the figure, which shows the results of a survey in which 1051 adults from France, 1042 adults from Germany, 1003 adults from the United Kingdom, and 1000 adults from the United States were asked whether national identity is strongly tied to birthplace. (Source: Pew Research Center)

National Identity Construct a 99% confidence interval for the population proportion of adults who say national identity is strongly tied to birthplace for each country listed.

Translating Statements In Exercises 29–34, translate the statement into a confidence interval. Approximate the level of confidence.

In a survey of 1502 U.S. adults, 31% said that they use Pinterest. The survey’s margin of error is ±2.9%. (Source: Pew Research Center)