Exam 10: Estimating Proportions With Confidence

In a survey of n = 100 people, 10% are left-handed. Using the "exact"formula for margin of error, calculate the margin of error for a 95% confidence interval.

Suppose a 95% confidence interval for the proportion of Americans who exercise regularly is 0.29 to 0.37. Which one of the following statements is false?

The general format for a confidence interval can be written as: sample estimate $\pm$ multiplier * standard error. In creating a confidence interval for a proportion, the standard error is:

Use the following information for questions: A television station plans to ask a random sample of 400 city residents if they can name the news anchor on the evening news at their station. They plan to fire the news anchor if fewer than 10% of the residents in the sample can do so. Suppose that 12% of city residents in the sample could name the anchor when asked. -Calculate a 95% confidence interval for the population proportion of city residents who can name the news anchor on the evening news at their station.

Use the following information for questions: Suppose that a 95% confidence interval for the proportion of first-year students at a school who played in intramural sports is 35% plus or minus 5%. -The confidence level for the confidence interval is

Use the following information for questions: In a nationwide survey of n = 1,030 adults, 6% answered yes to the question "During the last year did anyone break into or somehow illegally get into your home or apartment?" -A 98% confidence interval for the proportion of all Americans who had their homes broken into is

Use the following information for questions: A poll was conducted in order to get an idea of the demand for vegetarian meals at restaurants. The study was commissioned by the Vegetarian Resource Group and was published in the Vegetarian Today. A random sample of 1100 U.S. adults was asked whether or not they sometimes order a vegetarian dish (one without meat, fish, or fowl) when dining out. Those who conducted the survey collected many characteristics of the participants, including political party affiliation. In this sample, 600 identified themselves as Democrats and 500 identified themselves as Republicans. Of those sampled, 252 Democrats and 200 Republicans said that they sometimes order a dish without meat, fish, or fowl when they eat out. -Find a 95% confidence interval for the difference between the two population proportions of people that sometimes order a vegetarian meal when going out to eat. Let group 1 refer to Democrats and group 2 refer to Republicans.

Use the following information for questions: Random samples from two age groups of brides (200 brides under 18 years and 100 brides at least twenty years old) showed that 50% of brides in the under 18 group were divorced after 15 years, while 40% of brides in the 20 or older age group were divorced after 15 years. The difference between the two proportions is 0.10, with a standard error of 0.0604. -What is a 99% confidence interval for the difference between the population proportions of brides who are divorced within 15 years (brides under 18 - brides at least 20)?

In a randomly selected sample of 100 students at a University, 85% had use of a laptop computer. Calculate a 99% confidence interval for the proportion of all students who had use of a laptop computer.

Use the following information for questions: Suppose that a confidence interval for a population proportion p is to be calculated. For each sample size n and sample proportion $\hat{p}$ find the approximate margin of error for a 95% confidence interval ("the 95% margin of error"). -Sample size n = 100 and sample proportion $\hat{p}$ = 0.5

Use the following information for questions: A randomly selected sample of 400 students at a university with 15-week semesters was asked whether or not they think the semester should be shortened to 14 weeks (with longer classes). Forty-six percent of the 400 students surveyed answered yes. -Based on the sample data, what is the standard error of the sample proportion of students who answered yes to the question?

A 95% confidence interval for the proportion of women that has ever dozed off while driving is 0.07 to 0.14. For men, a 95% confidence interval for the proportion that has ever dozed off while driving is 0.19 to 0.25. Assume both intervals were computed using large random samples. What conclusion can be made about the population proportions that have dozed off while driving?

Suppose that 90%, 95%, 98%, and 99% confidence intervals are computed (using the same sample) for a population proportion. Which confidence level will give the narrowest interval?

Use the following information for questions: Suppose that a 95% confidence interval for the proportion of first-year students at a school who played in intramural sports is 35% plus or minus 5%. -The 95% confidence interval for the proportion of students playing intramural sports is

Use the following information for questions: A television station plans to ask a random sample of 400 city residents if they can name the news anchor on the evening news at their station. They plan to fire the news anchor if fewer than 10% of the residents in the sample can do so. Suppose that 12% of city residents in the sample could name the anchor when asked. -What is the value of the standard error of the sample proportion?

Use the following information for questions: In a nationwide survey of n = 1,030 adults, 6% answered yes to the question "During the last year did anyone break into or somehow illegally get into your home or apartment?" -A 95% confidence interval for the proportion of all Americans who had their homes broken into is

In a past General Social Survey, responses to the question "Have you ever been beaten or punched by another person" gave the following 95% confidence intervals for the population proportions of women and men who would say yes as 0.195 to 0.265 and 0.493 to 0.587, respectively. The sample sizes for men and women were large (444 men and 591 women). Is it reasonable to conclude that there is a difference in the population between men and women in the proportion that have ever been beaten or punched by another person?

Suppose that 200 different polling organizations and academic researchers all do surveys in which the same question is asked. All 200 research groups construct a 95% confidence interval for the proportion who would say "yes"to this question. About how many of the 200 different 95% confidence intervals will not capture the true population proportion?

Use the following information for questions: In a survey of n = 950 randomly selected individuals, 17% answered yes to the question "Do you think the use of marijuana should be made legal or not?" -A 90% confidence interval for the proportion of all Americans in favor of legalizing marijuana is

Use the following information for questions: Data is to be gathered to estimate the proportion of residents who will vote for Mr. Treehouse in the coming city election. A random sample of 650 voters is interviewed and 306 of them say that they will support Mr. Treehouse. -What is the value of the point estimate for the population proportion of residents who will vote for Mr. Treehouse in the coming city election?