8. Sampling Distributions & Confidence Intervals: Proportion

True or False? In Exercises 1 and 2, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

The point estimate for the population proportion of failures is 1-p^

Finding p^ and q^ In Exercises 3–6, let p be the population proportion for the situation. Find point estimates of p and q.

Social Security In a survey of 661 non-retired Americans, 218 said that they expect to rely on Social Security as major source of income when they retire. (Adapted from Gallup)

Finding p^ and q^ In Exercises 3–6, let p be the population proportion for the situation. Find point estimates of p and q.

Private Internet Browsing In a survey of 4272 U.S. adults, 1025 knew that private browsing mode only prevents someone using the same computer from seeing one’s online activities. (Adapted from Pew Research Center)

In Exercises 7–10, use the confidence interval to find the margin of error and the sample proportion.

(0.512, 0.596)

In Exercises 7–10, use the confidence interval to find the margin of error and the sample proportion.

(0.087, 0.263)

Constructing Confidence Intervals In Exercises 11 and 12, construct 90% and 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals.

New Year’s Resolutions In a survey of 1790 U.S. adults in a recent year, 816 have a New Year’s resolution related to their health. (Adapted from Finder)

Constructing Confidence Intervals In Exercises 13 and 14, construct a 99% confidence interval for the population proportion. Interpret the results.

New Year’s Resolutions In a survey of 1790 U.S. adults in a recent year, 816 have a New Year’s resolution related to their health. (Adapted from Finder)

LGBT Identification In a survey of 15,349 U.S. adults, 860 identify as lesbian, gay, bisexual, or transgender. Construct a 95% confidence interval for the population proportion of U.S. adults who identify as lesbian, gay, bisexual, or transgender. (Adapted from Gallup)

Bisexual Idenfitication In a survey of 692 lesbian, gay, bisexual, or transgender U.S adults, 378 said that they consider themselves bisexual. Construct a 90% confidence interval for the population proportion of lesbian, gay, bisexual, or transgender U.S. adults who consider themselves bisexual. (Adapted from Gallup)

Congress You wish to estimate, with 95% confidence, the population proportion of likely U.S. voters who think Congress is doing a good or excellent job. Your estimate must be accurate within 4% of the population proportion.

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

Congress You wish to estimate, with 95% confidence, the population proportion of likely U.S. voters who think Congress is doing a good or excellent job. Your estimate must be accurate within 4% of the population proportion.

b. Find the minimum sample size needed, using a prior survey that found that 21% of likely U.S. voters think Congress is doing a good or excellent job. (Source: Rasmussen Reports)

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.

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

Since 1935, the Gallup Organization has conducted public opinion polls in the United States and around the world. The table shows the results of Gallup’s World Affairs Poll of 2021, in which 1021 U.S. adults were polled. The remaining percentages not shown in the results are adults who were not sure.

b. What was the greatest value you obtained for p^?

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

In a survey of 880 unmarried U.S. adults who are living with a partner, 73% say love was a major reason why they decided to move in together. The survey’s margin of error is ±4.8%. (Source: Pew Research Center)

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

In a survey of 2094 U.S. adults who have used an online dating app, 57% said their personal experience with online dating was positive. The survey’s margin of error is ±3.6%. (Source: Pew Research Center)