Deck 10: Estimating Proportions With Confidence

Question 1

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 ____________.

A) sample; population
B) population; sample
C) neither

Answer 1

sample; population

Question 2

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.

-Sampling distributions take information from the ___________ to the ____________.

A) sample; population
B) population; sample
C) neither

Answer 2

population; sample

Question 3

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 ____________.

A) sample; population
B) population; sample
C) neither

Answer 3

sample; population

Question 4

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) sample; population
B) population; sample
C) neither

Question 5

Which statement is not true about confidence intervals?

A) A confidence interval is an interval of values computed from sample data that is likely to include the true population value.
B) An approximate formula for a 95% confidence interval is sample estimate $\pm$ margin of error.
C) A confidence interval between 20% and 40% means that the population proportion lies between 20% and 40%.
D) A 99% confidence interval procedure has a higher probability of producing intervals that will include the population parameter than a 95% confidence interval procedure.

Question 6

Which statement is not true about the 95% confidence level?

A) Confidence intervals computed by using the same procedure will include the true population value for 95% of all possible random samples taken from the population.
B) The procedure that is used to determine the confidence interval will provide an interval that includes the population parameter with probability of 0.95.
C) The probability that the true value of the population parameter falls between the bounds of an already computed confidence interval is roughly 95%.
D) If we consider all possible randomly selected samples of the same size from a population, the 95% is the percentage of those samples for which the confidence interval includes the population parameter.

Question 7

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

A) decrease the size of the population.
B) decrease the size of the sample.
C) increase the size of the population.
D) increase the size of the sample.

Question 8

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

A) decrease the size of the population.
B) decrease the size of the sample.
C) increase the size of the population.
D) increase the size of the sample.

Question 9

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

A) The confidence level.
B) The sample proportion.
C) The sample size.
D) The population size.

Question 10

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:

A) $\sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}$
B) 2 × $\sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}$
C) $\sqrt{\frac{1}{n}}$
D) $\sqrt{\frac{{p}(1 - p)}{n}}$

Question 11

In a poll of n = 200 randomly selected individuals, 60 people said they are opposed to the death penalty for persons convicted of murder. Which choice correctly shows the calculation of the margin of error for a 95% confidence interval for the population proportion opposed to the death penalty?

A) $\sqrt{\frac{1}{60}}$
B) 2 × $\sqrt{\frac{0.60(1-0.60)}{200}}$
C) 2 × $\sqrt{\frac{0.30(1-0.30)}{200}}$
D) 2 × $\sqrt{\frac{0.30(1-0.30)}{60}}$

Question 12

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?

A) It is a sample statistic.
B) It is a population parameter.
C) It is a margin of error.
D) It is a standard error.

Question 13

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?

A) point estimate
B) population parameter
C) sample estimate
D) sample statistic

Question 14

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?

Question 15

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?

Question 16

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?

Question 17

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

Question 18

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

A) 5%
B) 35%
C) 95%
D) None of the above

Question 19

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

A) 5%
B) 35%
C) 95%
D) None of the above

Question 20

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

A) 25% to 45%
B) 30% to 35%
C) 35% to 40%
D) 30% to 40%

Question 21

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

A) sample estimate
B) multiplier
C) standard error
D) none of the elements would be increased

Question 22

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

A) sample estimate
B) multiplier
C) standard error
D) none of the elements would be increased

Question 23

The multiplier for a confidence interval is determined by

A) the desired level of confidence and the sample size.
B) the desired level of confidence but not the sample size.
C) the sample size but not the desired level of confidence.
D) neither the sample size nor the level of confidence.

Question 24

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

A) 0.05
B) 0.10
C) 0.25
D) 0.50

Question 25

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

A) 0.062
B) 0.084
C) 0.123
D) 0.228

Question 26

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

A) 0.0003
B) 0.011
C) 0.025
D) 0.030

Question 27

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

A) 0.8365
B) 2.26
C) 2.33
D) None of the above

Question 28

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

A) 1.28
B) 0.840
C) 0.788
D) None of the above

Question 29

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

A) 0.580
B) 0.764
C) 1.08
D) None of the above

Question 30

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 60% confidence interval is

A) 0.84
B) 0.7995
C) 0.99
D) None of the above

Question 31

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

A) 0.048 to 0.072
B) 0.045 to 0.075
C) 0.043 to 0.077
D) 0.041 to 0.079

Question 32

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 99% confidence interval for the proportion of all Americans who had their homes broken into is

A) 0.048 to 0.072
B) 0.045 to 0.075
C) 0.043 to 0.077
D) 0.041 to 0.079

Question 33

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

A) 0.048 to 0.072
B) 0.045 to 0.075
C) 0.043 to 0.077
D) 0.041 to 0.079

Question 34

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

A) 0.048 to 0.072
B) 0.045 to 0.075
C) 0.043 to 0.077
D) 0.041 to 0.079

Question 35

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

A) 0.150 to 0.190
B) 0.146 to 0.194
C) 0.142 to 0.198
D) 0.139 to 0.201

Question 36

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

A) 0.150 to 0.190
B) 0.146 to 0.194
C) 0.142 to 0.198
D) 0.139 to 0.201

Question 37

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

A) 0.150 to 0.190
B) 0.146 to 0.194
C) 0.142 to 0.198
D) 0.139 to 0.201

Question 38

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

A) 0.150 to 0.190
B) 0.146 to 0.194
C) 0.142 to 0.198
D) 0.139 to 0.201

Question 39

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

A) 0.852 to 0.888
B) 0.849 to 0.891
C) 0.845 to 0.895
D) 0.842 to 0.898

Question 40

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 99% confidence interval for the proportion of all Americans who approve of punching an intruder is

A) 0.852 to 0.888
B) 0.849 to 0.891
C) 0.845 to 0.895
D) 0.842 to 0.898

Question 41

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 90% confidence interval for the proportion of all Americans who approve of punching an intruder is

A) 0.852 to 0.888
B) 0.849 to 0.891
C) 0.845 to 0.895
D) 0.842 to 0.898

Question 42

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

A) 0.852 to 0.888
B) 0.849 to 0.891
C) 0.845 to 0.895
D) 0.842 to 0.898

Question 43

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?

A) There is a 95% probability that the true proportion of young adults who skip breakfast is between 0.20 and 0.27.
B) In about 95% of all studies for which this procedure is used, the confidence interval will cover the true population proportion, but there is no way to know if this interval covers the true proportion or not.
C) If this study were to be repeated with a sample of the same size, there is a 95% probability that the sample proportion would be between 0.20 and 0.27.
D) The proportion of young adults who skip breakfast 95% of the time is between 0.20 and 0.27.

Question 44

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 the correct interpretation of the 95% confidence interval?

A) There is a 95% probability that the proportion of young adults who skip breakfast is between 0.20 and 0.27.
B) If this study were to be repeated with a sample of the same size, there is a 95% probability that the sample proportion would be between 0.20 and 0.27.
C) We can be 95% confident that the sample proportion of young adults who skip breakfast is between 0.20 and 0.27.
D) We can be 95% confident that the population proportion of young adults who skip breakfast is between 0.20 and 0.27.

Question 45

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

A) $\hat{p}$ = 0.235 and margin of error = 0.035.
B) $\hat{p}$ = 0.235 and margin of error = 0.07.
C) p = 0.235 and margin of error = 0.035.
D) p = 0.235 and margin of error = 0.07.

Question 46

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?

A) 0.10
B) 0.05
C) 0.04
D) 0.025

Question 47

A sample of n = 168 students was asked, "Do you believe in love at first sight?" The choices below show confidence intervals, in scrambled order, for 90%, 95%, 98%, and 99% confidence levels for the population proportion who would answer yes. Which choice gives the 99% confidence interval?

A) 0.56 to 0.68
B) 0.52 to 0.72
C) 0.53 to 0.71
D) 0.55 to 0.69

Question 48

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?

A) 0
B) 5
C) 10
D) 190

Question 49

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.

A) 0.03
B) 0.05
C) 0.06
D) 0.10

Question 50

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?

A) 99%
B) 98%
C) 95%
D) 90%

Question 51

You plan to use a conservative margin of error of 2%. How large a sample size do you need?

A) 100
B) 400
C) 2500
D) None of the above

Question 52

You plan to determine an approximate 95% confidence interval for a population proportion; you plan to use a conservative margin of error of 10%. How large a sample size do you need?

A) 100
B) 400
C) 2500
D) None of the above

Question 53

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?

A) 100
B) 400
C) 1600
D) 2500

Question 54

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?

A) 100
B) 400
C) 2500
D) None of the above

Question 55

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

A) the true proportion p is close to 0.
B) the true proportion p is close to 1.
C) the true proportion p is close to .5.
D) the true proportion p is close to the sample proportion $\hat{p}$ .

Question 56

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?

A) 90%
B) 98%
C) It depends on the value of the sample proportion.
D) It depends on the value of the true population proportion.

Question 57

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 point estimate of p equals 0.40.

Question 58

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.

Question 59

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.

Question 60

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%.

Question 61

Explain what a margin of error of 5% means for a survey result if 35% of the people from a random sample are overweight.

Question 62

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

Question 63

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").

Question 64

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").

Question 65

In a past General Social Survey, 23% of a random sample of 591 women 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").

Question 66

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.

Question 67

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.

Question 68

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.

Question 69

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.

Question 70

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?

Question 71

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 standard error of the sample proportion?

Question 72

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 < p < 0.2875) = 0.95?

Question 73

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?

Question 74

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?

Question 75

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?

Question 76

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 point estimate for the population proportion of city residents who can name the news anchor on the evening news at their station?

Question 77

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?

Question 78

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.

Question 79

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.
-Explain in your own words what the 95% confidence level implies.

Question 80

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?