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 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 90% confidence interval for the population proportion of teen drivers who were not involved in a car accident based on this data?

Which statement is not true about confidence intervals?

In a recent poll of 500 13-year-olds, many indicated to enjoy their relationships with their parents. Suppose that 200 of the 13-year olds were boys and 300 of them were girls. We wish to estimate the difference in proportions of 13-year old boys and girls who say that their parents are very involved in their lives. In the sample, 93 boys and 172 girls said that their parents are very involved in their lives. What is a 96% confidence interval for the difference in proportions (proportion of boys minus proportion of girls)?

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 standard error of the sample proportion $\hat{p}$ is equal to 0.0714.

In a past General Social Survey, 54% of a random sample of 444 men answered yes to the question," Have you ever been punched or beaten by another person?" Calculate an approximate 95% confidence interval for the proportion of all Americans who have been punched. Use the approximate margin of error (or the "95% margin of error").

Which of the following is the minimum sample size that could be used to guarantee that the margin of error for a confidence interval for a proportion is no more than 0.025?

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 98% confidence interval for the proportion of all Americans in favor of legalizing marijuana is

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. -Which of the following is a correct interpretation of the 95% confidence level?

What is the fundamental rule for data inference, or what property must samples have before valid inferences can be made about the population?

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. -Statistical inference takes 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 confidence level find the appropriate z* multiplier. -The z* multiplier for a 72% confidence interval is

Use the following information for questions: In a past General Social Survey, 87% of a random sample of n = 990 respondents answered yes to the question "Would you approve of an adult male punching a stranger if the stranger had broken into the man's house?" -A 95% confidence interval for the proportion of all Americans who approve of punching an intruder is

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 99% confidence interval for the proportion of all Americans in favor of legalizing marijuana is

In a past General Social Survey, 37% of a random sample of n = 1035 respondents answered yes to the question, "Have you ever been punched or beaten by another person?" Calculate an approximate 95% confidence interval for the proportion of all Americans who have been punched: use the approximate margin of error (or the "95% margin of error").

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. -In the article that was published in Vegetarian Today, the author wrote, "The 95% confidence level tells us that if the same survey were repeated 100 times, 95 times the same responses would be returned." Is this a correct interpretation of the 95% confidence level?

Use the following information for questions: In a past General Social Survey, 87% of a random sample of n = 990 respondents answered yes to the question "Would you approve of an adult male punching a stranger if the stranger had broken into the man's house?" -A 98% confidence interval for the proportion of all Americans who approve of punching an intruder is

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 estimate for the difference between the proportions of men with and without a college degree who use e-mail often?

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

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). -There is a 95% probability that the population proportion of supermarket customers who do not buy house-brand products at all lies between 18% and 46%.