Exam 10: Estimating Proportions With Confidence

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. -What is the estimate for the difference between the proportions of female and male students who have a job while going to college?

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 = 60 and sample proportion $\hat{p}$ = 0.35

Use the following information for questions: Many people now-a-days use e-mail to communicate with family and friends and as a primary source of communication at their job. Is there a difference between the use of e-mail for men with a college education and those without? A survey in a large city reveals that out of 230 males with a college degree, 212 use e-mail more than twice a day. Out of the 150 without a college education, 122 use e-mail more than twice a day. -What is the standard error of the estimate?

When creating a confidence interval for a proportion the conservative margin of error (studied in Chapter 5) and the margin of error found by taking 2 standard errors are closest to each other when

In a past General Social Survey, a random sample of men and women 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 0.13 to 0.19 for women and 0.25 to 0.33 for men. Based on these results, you can reasonably conclude that

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. -A census takes information from the ___________ to the ____________.

A poll is done to estimate the proportion of adult Americans who like their jobs. The poll is based on a random sample of 400 individuals. What is the "conservative" margin of error of this poll?

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

You plan to determine an approximate 95% confidence interval for a population proportion; you plan to use a conservative margin of error of 5%. How large a sample size do you need?

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). -What is the value of the point estimate for the population proportion of teen drivers who were involved in a car accident?

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 statements about the number 46% is correct?

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 80% confidence interval is

In a randomly selected sample of 500 students at a University, 80% say they plan to graduate within 4 years. Calculate a 95% confidence interval for the proportion of all students who plan to graduate within 4 years.

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 90% confidence interval for the proportion of all Americans who had their homes broken into is

Use the following information for questions: A 95% confidence interval for p the proportion of supermarket customers who do not buy house-brand products at all is calculated and turns out to be: (0.18, 0.46). -The above confidence interval was constructed with a margin of error of 14 percentage points.

In the Youth Risk Behavior Survey (a study of public high school students), a random sample showed that 45 of 675 girls and 103 of 621 boys had been in a physical fight on school property one or more times during the past 12 months. What is an approximate 95% confidence interval for the difference in proportions of students who had been in a fight (proportion of boys minus proportion of girls)?

Explain what a confidence level of 95% means in a 95% confidence interval.

Which of the following quantities does not affect the width of a confidence interval?

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 proportion of students who answered yes to the question was 36% instead of 46%, would the margin of error be smaller or larger?

Use the following information for questions: A 95% confidence interval for the proportion of young adults who skip breakfast is found to be 0.20 to 0.27. -From the information provided, we can determine that