Question 1

Use the following information for questions:
 The next  question are based on a survey of 500 students living in campus dormitories. Questionnaires were mailed to each of the 500 students. The questionnaire asked if they had ever stolen a bicycle or not. The sample proportion who said they had stolen a bicycle was used to estimate the proportion of all students on campus who had ever stolen a bicycle.
-Describe why selection bias is a problem for this survey.

Accepted Answer

The answer of Use the following information for questions:
 The...

Question 2

Use the following information for questions:
 The next  question are based on a survey of 500 students living in campus dormitories. Questionnaires were mailed to each of the 500 students. The questionnaire asked if they had ever stolen a bicycle or not. The sample proportion who said they had stolen a bicycle was used to estimate the proportion of all students on campus who had ever stolen a bicycle.
-Describe why response bias could be a problem for this survey.

Accepted Answer

The answer of Use the following information for questions:
 The...

Question 3

Use the following information for questions:
 The next  question are based on a survey of 500 students living in campus dormitories. Questionnaires were mailed to each of the 500 students. The questionnaire asked if they had ever stolen a bicycle or not. The sample proportion who said they had stolen a bicycle was used to estimate the proportion of all students on campus who had ever stolen a bicycle.
-Describe why non-response bias could be a problem for this survey.

Accepted Answer

The answer of Use the following information for questions:
 The...

Question 4

A survey is planned to be done by contacting a random sample of people who have bought something over the Internet; the question would ask whether sales made over the Internet should be taxed or not. The purpose is to estimate the proportion of all Americans who would support an Internet sales tax. Explain why selection bias would be a problem for this survey.

Accepted Answer

The answer of A survey is planned to be done...

Question 5

A random sample of registered 500 voters was taken, and 80% responded that they had voted in the last presidential election. Explain why response bias may be a problem for this survey.

Accepted Answer

The answer of A random sample of registered 500 voters...

Question 6

A telephone survey was planned to ask people whether they planned to watch the next Super Bowl. Explain why non-response bias may be a problem for this survey.

Accepted Answer

The answer of A telephone survey was planned to ask...

Question 7

Studies have shown that growing numbers of young girls are beginning to use steroids. At a committee hearing, a survey by the Centers for Disease Control and Prevention of high school students was cited, in which 7.3 percent of ninth-grade girls said they had used illegal steroids. One critic of the results objected to the methodology of the survey, which used an anonymous questionnaire and did not ask what substances were used. He suggested that some of the teenagers might have thought incorrectly that were using anabolic steroids. What type of bias is being raised by this issue?

Accepted Answer

The answer of Studies have shown that growing numbers of...

Question 8

Which one of the following statements is true about sample size and margin of error?
A) Increasing the sample size of a survey decreases the margin of error.
B) Increasing the sample size of a survey increases the margin of error.
C) Increasing the sample size of a survey does not change the margin of error.
D) Increasing the sample size of a survey only changes the margin of error if there is an error (a mistake) in the way the survey is conducted.

Accepted Answer

Increasing the sample size of a survey decreases the margin of error because a larger sample provides more information and reduces uncertainty in the estimate.

Question 9

A randomly selected sample of 1,000 college students was asked whether they had ever used the drug Ecstasy. Sixteen percent (16% or 0.16) of the 1,000 students surveyed said they had. Which one of the following statements about the number, 0.16 is correct?
A) It is a sample proportion.
B) It is a population proportion.
C) It is a margin of error.
D) It is a randomly chosen number.

Accepted Answer

The number 0.16 represents the proportion of students in the sample who said they had used Ecstasy, making it a sample proportion.

Question 10

A random sample of Americans at least 65 years old showed that 32% believe their health is extremely important. If the sample size was 100, approximately what was the margin of error?
A) 1%
B) 5%
C) 10%
D) 15%

Accepted Answer

The answer of A random sample of Americans at least...

Question 11

A random sample of 1001 Americans aged 18-24 years showed that 51% believe their health is extremely important. An approximate 95% confidence interval for the proportion of all 18-24 year olds who believe that their health is extremely important is
A) between 41% and 61%.
B) between 46% and 56%.
C) between 48% and 54%.
D) between 50% and 52%.

Accepted Answer

The 95% confidence interval for a proportion is calculated using the formula: p ± Z * sqrt(p(1-p)/n), where p is the sample proportion, Z is the Z-score for 95% confidence (approximately 1.96), and n is the sample size. For p = 0.51 and n = 1001, the interval is approximately between 48% and 54%.

Question 12

A random sample of Americans showed that 4% believe their health care is excellent. If the conservative margin of error was 12.5%, what was the sample size?
A) 25
B) 36
C) 49
D) 64

Accepted Answer

The margin of error (MOE) in a proportion is calculated using the formula MOE = Z * sqrt(p(1-p)/n), where Z is the Z-score corresponding to the confidence level (not provided, but not needed for this calculation), p is the proportion (0.04 in this case), and n is the sample size. Rearranging the formula to solve for n gives n = p(1-p) / (MOE/Z)^2. Given that the MOE is 12.5% or 0.125, and using the proportion of 0.04, we don't need the exact Z-score to solve for n because the question implies a conservative estimate, which typically means using a higher Z-score to ensure the margin of error encompasses the true proportion. Plugging the values into the rearranged formula without explicitly solving for Z, we aim to find a sample size (n) that fits the given MOE. Without direct calculation, the correct answer must be chosen from the options provided, and given the relationship between MOE and sample size (larger sample sizes give smaller MOEs), we infer that a larger sample size is needed for a relatively small MOE of 12.5% when the proportion is also small (4%). Among the provided options, 64 (D) is the largest sample size and thus the most likely to produce the given MOE under these conditions.

Question 13

A Gallup poll reported that 88% of Americans say they have health insurance. If the sample size was 2500, an approximate 95% confidence interval for the proportion of all Americans who say they are insured is
A) between 80% and 96%.
B) between 84% and 92%.
C) between 86% and 90%.
D) between 87.3% and 88.7%.

Accepted Answer

The answer of A Gallup poll reported that 88% of...

Question 14

A Gallup poll reported that 58% of Americans say they are satisfied with the costs of healthcare. If the margin of error was 5%, approximately what was the sample size?
A) 10
B) 200
C) 400
D) 1600

Accepted Answer

The sample size can be calculated using the formula for the margin of error in a proportion: $ME = Z \sqrt{\frac{p(1-p)}{n}}$, where ME is the margin of error, Z is the Z-score for the desired confidence level (typically 1.96 for 95% confidence), p is the proportion (0.58 in this case), and n is the sample size. Rearranging to solve for n gives $n = \frac{Z^2 p(1-p)}{ME^2}$. Plugging in the values (with ME = 0.05 and assuming a 95% confidence level so Z = 1.96), we get a sample size close to 400.

Question 15

Use the following information for questions:
 According to a Gallup poll, about 90% of all American adults owned a cell phone at the time of the poll. The results are based on telephone interviews with a randomly selected national sample of 998 adults, 18 years and older. The margin of error was reported to be 3.5%.
-What was the population of interest in this Gallup Poll?
A) All American adults who own cell phones.
B) All American adults.
C) The 998 adults who participated in the survey.
D) The participants in the survey who owned cell phones.

Accepted Answer

The population of interest refers to the entire group about whom the poll seeks to draw conclusions, which in this case is all American adults, regardless of whether they own a cell phone or not.

Question 16

Use the following information for questions:
 According to a Gallup poll, about 90% of all American adults owned a cell phone at the time of the poll. The results are based on telephone interviews with a randomly selected national sample of 998 adults, 18 years and older. The margin of error was reported to be 3.5%.
-Which of the following statements correctly interprets the reported margin of error of 3.5%?
A) In about 95% of all random samples of this size from the same population, the difference between the sample percent and the population percent will be less than 3.5%.
B) In about 3.5% of all random samples of this size from the same population, the sample percent will equal the population percent.
C) The probability that a 95% confidence interval based on this poll does not cover the population proportion is 3.5%.
D) In about 95% of all random samples of this size from the same population, the difference between the sample percent and the population percent will be more than 3.5%.

Accepted Answer

The margin of error in polling data indicates the range within which the true population parameter is expected to lie with a certain level of confidence. Statement A correctly interprets the margin of error as meaning that for 95% of all random samples of the same size from the same population, the difference between the sample percentage and the true population percentage will be less than 3.5%.

Question 17

A recent poll reported that 62% of all college students believe there is extraterrestrial life. The 95% margin of error for the poll was 4%. Which of the following statements is correct?
A) We can be certain that the percentage of all college students who believe there is extraterrestrial life is in the interval 58% to 66%.
B) The chance is 95% that at least 62% of all college students believe there is extraterrestrial life.
C) With 95% confidence we can say that the percentage of all college students who believe there is extraterrestrial life is between 58% and 66%.
D) The chance is 5% that at least 62% of all college students believe there is extraterrestrial life.

Accepted Answer

The correct statement is C because a margin of error in polling indicates the range within which the true value is expected to lie with a certain level of confidence. In this case, with a 95% confidence level, the true percentage of all college students who believe in extraterrestrial life is estimated to be between 58% (62% - 4%) and 66% (62% + 4%).

Question 18

A polling agency conducted a survey of 100 doctors on the question: "Are you willing to treat women patients with the recently approved pill RU-486?" The conservative margin of error associated with the 95% confidence interval for the percent who say 'yes' is
A) 50%.
B) 10%.
C) 5%.
D) 2%.

Accepted Answer

The margin of error in a survey is influenced by the sample size and the confidence level. For a sample size of 100 and a 95% confidence level, a common approximation for the margin of error is around 10%. This is because the maximum margin of error for a proportion (when p=0.5) using a 95% confidence level is approximately 1/sqrt(n), where n is the sample size. For n=100, this calculation gives us about 0.1 or 10%.

Question 19

In a random sample of n = 400 people, 40% say they have allergies. The conservative margin of error is reported to be 5%. What is a 95% confidence interval for the percent of the population that has allergies?
A) 25% to 55%
B) 30% to 50%
C) 35% to 45%
D) 40% to 45%

Accepted Answer

The sample proportion is 40%, and the margin of error is 5%. Therefore, the confidence interval is 40% ± 5%, which is 35% to 45%.

Question 20

Which one of the following statements is true?
A) Increasing the sample size of a survey decreases the margin of error.
B) Increasing the sample size of a survey increases the margin of error.
C) Increasing the sample size of a survey decreases the impact of response bias.
D) Increasing the sample size of a survey increases the impact of response bias.

Accepted Answer

Increasing the sample size of a survey generally decreases the margin of error, making the survey results more precise and reliable. This is because a larger sample size better represents the population, reducing the variability in the estimates.

Quiz 5: Sampling: Surveys and How to Ask Questions

A random sample of registered 500 voters was taken, and 80% responded that they had voted in the last presidential election. Explain why response bias may be a problem for this survey.

A telephone survey was planned to ask people whether they planned to watch the next Super Bowl. Explain why non-response bias may be a problem for this survey.

Which one of the following statements is true about sample size and margin of error?

A randomly selected sample of 1,000 college students was asked whether they had ever used the drug Ecstasy. Sixteen percent (16% or 0.16) of the 1,000 students surveyed said they had. Which one of the following statements about the number, 0.16 is correct?

A random sample of Americans at least 65 years old showed that 32% believe their health is extremely important. If the sample size was 100, approximately what was the margin of error?

A random sample of 1001 Americans aged 18-24 years showed that 51% believe their health is extremely important. An approximate 95% confidence interval for the proportion of all 18-24 year olds who believe that their health is extremely important is

A random sample of Americans showed that 4% believe their health care is excellent. If the conservative margin of error was 12.5%, what was the sample size?

A Gallup poll reported that 88% of Americans say they have health insurance. If the sample size was 2500, an approximate 95% confidence interval for the proportion of all Americans who say they are insured is

A Gallup poll reported that 58% of Americans say they are satisfied with the costs of healthcare. If the margin of error was 5%, approximately what was the sample size?

A recent poll reported that 62% of all college students believe there is extraterrestrial life. The 95% margin of error for the poll was 4%. Which of the following statements is correct?

A polling agency conducted a survey of 100 doctors on the question: "Are you willing to treat women patients with the recently approved pill RU-486?" The conservative margin of error associated with the 95% confidence interval for the percent who say 'yes' is

In a random sample of n = 400 people, 40% say they have allergies. The conservative margin of error is reported to be 5%. What is a 95% confidence interval for the percent of the population that has allergies?

Which one of the following statements is true?