Exam 10: Estimating Proportions With Confidence

A random sample of 600 adults is taken from a population of over one million, in order to compute a confidence interval for a proportion. If the researchers wanted to decrease the width of the confidence interval, they could

Use the following information for questions: Suppose that a confidence interval for a population proportion p is to be calculated. For each confidence level find the appropriate z* multiplier. -The z* multiplier for a 98% confidence interval is

Use the following information for questions: In a past General Social Survey, 22% of n = 1006 respondents answered yes to the question "Are you a member of any sports groups?" A 95% confidence interval for the population proportion of Americans who belonged to a sports group at that time is 19.4% to 24.6%. -Based on these results, you can reasonably conclude that

The following ranges are possible 95% confidence intervals for the percentage of Americans who think they work too many hours. For which one of the confidence intervals could you conclude that a majority of the population thinks they work too many hours?

In a past General Social Survey, a random sample of respondents answered the question "Are you a member of any sports groups?" Based on the sample data, 95% confidence intervals for the population proportion who would answer yes are 0.215 to 0.365 for people 18 to 23 years old and 0.247 to 0.333 for people 24 to 29 years old. Based on these results, you can reasonably conclude that

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. -Which one of the following description of the number 46% is not correct?

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 95% confidence interval for the proportion of all Americans in favor of legalizing marijuana is

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 margin of error for the confidence interval is

Use the following information for questions: Some statistical procedures move from population to sample; some move from sample to population. For each of the following procedures, determine the correct direction. -Confidence intervals take information from the ___________ to the ____________.

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 = 1000 and sample proportion $\hat{p}$ = 0.35

If the confidence level is increased, which of the following must also be increased?

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. -If the sample consisted of 300 students instead of 400 students, but the sample proportion of students who answered yes to the question was still 46%, would the margin of error be smaller or larger?

For a randomly selected sample of 40 first-year students at a University, 20% received a grade of A in their required course in English. Calculate a 90% confidence interval for the proportion of all first-year students who received an A in English.

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 95% confidence interval for the difference between the population proportions of brides who are divorced within 15 years (brides under 18 - brides at least 20)?

Use the following information for questions: A survey at a large public university reveals that many students hold a (part-time) job while going to college. Out of 127 female students surveyed, 95 have a job and out of 143 male students, 97 have a job. -Calculate a 95% confidence interval for the difference in proportions.

An Anti-Smoking organization wishes to determine what percentage of students in the state of Pennsylvania smoke cigarettes at least once a day. The organization will randomly sample 2400 students. In the sample they obtain, 450 students say they smoke cigarettes at least once a day. Calculate a 95% confidence interval for the proportion of all students in the state of Pennsylvania that smoke cigarettes at least once a day.

Use the following information for questions: Suppose that a 95% confidence interval for the proportion of teen drivers who were involved in a car accident is found to be (0.1425, 0.2875). -Consider the following statement: "If the sampling procedure were repeated many times, this would result in many different 95% confidence intervals. We would expect that 95% of the time, the true value of the population proportion would fall between 0.1425 and 0.2875." Does this statement correctly interpret the meaning of the 95% confidence level?

Use the following information for questions: Suppose that a 95% confidence interval for the proportion of teen drivers who were involved in a car accident is found to be (0.1425, 0.2875). -Does the 95% confidence level imply that P(0.1425 < $\hat{p}$ < 0.2875) = 0.95?

A study was conducted to learn about the proportions of U.S. residents who do not have medical insurance. Independent random samples of 942 U.S. women and 754 U.S. men were obtained. Of those sampled, 181 women and 181 men said that they do not have medical insurance. Calculate a 90% confidence interval for the difference in proportions (proportion of men minus proportion of women).

If the sample size is increased but the sample proportion remains the same, which of the following must also be increased?