Deck 7: Survey Sampling and Inference

Question 1

Use the following information to answer questions (6)-(8). A marble manufacturer advertises that its bags
of marbles will contain 25% "milky-white" marbles. Suppose that a bag containing 80 marbles is
inspected.
What is the standard error? Round to the nearest tenth of a percent.

Answer 1

4.8%

Question 2

Suppose the event planner assumes that 2.8% of the children attending the event will be lactose intolerant so he orders 7 lactose-free meals. What is the approximate probability that more than 2.8% of the children attending the event are lactose intolerant and that he will not have enough lactose-free meals? Round to the nearest thousandth.

Answer 2

0.103

Question 3

A survey of 800 randomly selected senior citizens showed that 55% said they planned to watch an upcoming political debate on television. The margin of error for the 95% confidence interval is 3.5 percentage points. Does the confidence interval support the claim that the majority of senior citizens plan to watch the upcoming political debate on television? Explain why or why not.

Answer 3

Yes, a confidence interval of 55% 3.5% would include plausible population parameter values that are greater than 50% so the claim would not be unreasonable.

Question 4

Suppose the event planner assumes that only 0.8% of the children attending the event will be lactose intolerant so he orders 2 lactose-free meals. What is the approximate probability that he will have too many lactose-free meals? Round to the nearest thousandth.

Question 5

Suppose a city manager conducts a poll and finds that a 95% confidence interval for the proportion of residents who support parking restrictions during snow removal periods as 63% to 71%. Explain what this confidence interval means - the 95% and what the interval represents.

Question 6

A polling agency wants to estimate the proportion of U.S. citizens who support the president's educational policies. They surveyed 1500 U.S. citizens and found a 95% confidence interval for the difference in proportions between men and women who support the president's educational policies as (-0.075 to 0.025) where population 1 is men and population 2 is women. Interpret the result and state if the assumptions are satisfied.

Question 7

Confidence intervals can be used to determine whether different sample proportions reflect a "real" difference in the population. Explain the method of how this is accomplished and what the assumptions are.

Question 8

Explain the difference between a statistic and a parameter. Give an example of each.

Question 9

Suppose that you and a friend read the following statement in a news report, "A recent poll found that 54% of voters, give or take 3%, plan to vote for candidate X in the next election (with a confidence level of 95%)". Your friend then makes the statement, "Hey, look, there's a 95% chance that somewhere between 51% and 57% of voters plan to vote for candidate X!" How would you explain to your friend why his statement is incorrect, be sure to provide your friend with the correct interpretation of the confidence interval.

Question 10

On average, how many of the children attending the event would be expected to be lactose intolerant, give or take how many? Round to the nearest whole person.

Question 11

Explain the difference between the standard error of a sample proportion and the margin of error of a confidence interval for a population proportion.

Question 12

Explain the difference between a population and a sample. Give an example of each.

Question 13

Describe the importance of how survey questions are phrased - in particular, the effect on the sample results. Explain how such a sample may not be reflective of the population.

Question 14

A sampling method should be as precise and accurate as possible. Explain what these two terms mean and how each is measured.

Question 15

Use the following information to answer questions (15)-(16). In a recent poll of 900 randomly selected adults, 37%
reported that they could not swim 24 yards (the length of a typical gymnasium lap pool).
Report the 95% confidence interval for the proportion of adults who self-report that they cannot swim 24 yards. Round final calculations to the nearest tenth of a percent.

Question 16

Suppose that Michigan lawmakers survey 500 randomly selected registered voters to see if they favor an extension of the fall duck hunting season. The lawmakers believe the population proportion in favor of extending the duck hunting season is 45% (based on historical data and previous votes). State the three conditions of the Central Limit Theorem and explain whether each condition is satisfied in this scenario.

Question 17

Use the following information to answer questions (6)-(8). A marble manufacturer advertises that its bags
of marbles will contain 25% "milky-white" marbles. Suppose that a bag containing 80 marbles is
inspected.
What value should we expect for our sampling percentage of milky-white marbles? How many marbles would this be? Round to the nearest whole marble.

Question 18

Use the following information to answer questions (6)-(8). A marble manufacturer advertises that its bags
of marbles will contain 25% "milky-white" marbles. Suppose that a bag containing 80 marbles is
inspected.
Use your answers to fill in the blanks: We expect % milky-white marbles, give or take %

Question 19

Frederick is interested in whether residents of his community are opposed to the construction of a party store on the corner of a busy inter

Question 20

Use the following information to answer questions (15)-(16). In a recent poll of 900 randomly selected adults, 37%
reported that they could not swim 24 yards (the length of a typical gymnasium lap pool).
What is the margin of error, using a 95% confidence level, for estimating the true proportion of adults who self-report that they cannot swim 24 yards? Round to the nearest thousandth.

Question 21

Confidence intervals can be used to determine whether different sample proportions reflect a "real" difference in the population. The basic approach is to

A)find the margin of error for each proportion and see if the difference is less than zero.
B)find the difference in the proportions and see if the difference is less than zero.
C)find a confidence interval at the significance level desired for the difference in proportions.
D)find the difference in the proportions and see if the difference is greater than zero.

Question 22

Use the following information to answer questions (14)-(15). In a recent poll of 1100 randomly selected home
delivery truck drivers, 26% said they had encountered an aggressive dog on the job at least once.
What is the margin of error, using a 95% confidence level, for estimating the true population proportion of home delivery truck drivers who have encountered an aggressive dog on the job at least once? (Round to the nearest thousandth)

A)0.026
B)0.013
C)0.004
D)0.053

Question 23

Which of the following statements is true about the confidence interval for a population proportion?

A)The confidence interval for a proportion will always contain the true population proportion.
B)The confidence interval for a proportion does not need a specified confidence level.
C)It is equal to the population proportion plus or minus the standard error.
D)It is equal to the sample proportion plus or minus a calculated amount called the margin of error.

Question 24

A factory manager is monitoring the quality of production of a small battery powered toy. The factory produces 600 toys in an hour. Thirty toys are tested from each hour's production. Which one of the following statements is the most accurate?

A)The toys being tested are the sample and the sample size is 30.All toys produced in that hour is the population.
B)The toys being tested are the population.All toys produced in that hour is the sample and the sample size is 600.
C)The toys being tested are the sample.The factory's total production is the population.
D)None of these statements accurately describe this situation.

Question 25

Use the following information to answer questions (14)-(15). In a recent poll of 1100 randomly selected home
delivery truck drivers, 26% said they had encountered an aggressive dog on the job at least once.
What is the standard error for the estimate of the proportion of all home delivery truck drivers who have encountered an aggressive dog on the job at least once? Round to the nearest ten-thousandth.

A)0.1322
B)0.0132
C)0.0002
D)0.0141

Question 26

Complete the statement by filling in the blank. When constructing a confidence interval, if the level of confidence decreases, the margin of error will and the confidence interval will be .

A)Decrease, wider.
B)Decrease, narrower.
C)Increase; wider.
D)Increase; narrower.

Question 27

Which of the following statements is not true about a sampling distribution?

A)It gives probabilities for a statistic.
B)It gives characteristics of the estimator, such as bias and precision.
C)It is used for making inferences about a sample.
D)It is the probability distribution of a statistic.

Question 28

Suppose that the age of all the U. S. vice presidents when they took office was recorded. The collection of the ages of all the U. S. vice presidents when they took office is a .

A)Population
B)Sample
C)Parameter
D)Statistic

Question 29

Researchers are interested in learning more about the age of men when they marry for the first time so they survey 500 married or divorced men and ask them how old they were when they first married. The mean age of the 500 men when they married for the first time would be a .

A)Population
B)Sample
C)Parameter
D)Statistic

Question 30

If it is being used to make inferences about a population, a good statistic (or estimator) should

A)Be accurate and precise.
B)Show correlation.
C)Always equal the population parameter.
D)All of the above.

Question 31

Suppose that Illinois lawmakers survey 130 randomly selected registered voters to see if they favor charging a deposit on aluminum cans to encourage recycling. The lawmakers believe the population proportion in favor of changing the law is 93% (based on historical data and previous votes). Which of the following conditions for the Central Limit theorem are not met?

A)The population proportion is too small and will not have enough expected failures.
B)Relative to the population, the sample is not large enough.
C)The population proportion is too small and will not have enough expected successes.
D)None of the above, all the condition of the CLT are met.

Question 32

The mean age of all the U. S. vice presidents when they took office would be a .

A)Population
B)Sample
C)Parameter
D)Statistic

Question 33

All daily maximum temperatures in August last year for all major U.S. cities were recorded. The mean of all maximum temperatures would be a _____________.

A)Population
B)Sample
C)Parameter
D)Statistic

Question 34

A group of screwdrivers produced in a day at a particular factory has a defect rate of 0.7%. Suppose a quality inspector randomly inspects 500 screwdrivers. Complete the following statement: The quality inspector should expect ____defective screwdrivers, with an error of ____.

A)35; 0.4%
B)3.5; 0.4%
C)1; 4.0%
D)1; 0.4%

Question 35

A polling agency wants to estimate the proportion of U.S. citizens who support the president's domestic policies. They surveyed 2500 U.S. citizens and found a 95% confidence interval for the difference in proportions between men and women who support the president's domestic policies as (-0.025 to 0.050) where population 1 is men and population 2 is women. Select the correct interpretation of this result.

A)The interval contains zero which shows that women are more likely than men to disagree with the president's foreign policies.
B)The interval contains zero which shows that men are more likely than women to disagree with the president's foreign policies.
C)The interval does not contain zero which shows that there is no significant difference in the proportions between men and women.
D)The interval contains zero which shows that there is no significant difference in the proportions between men and women.

Question 36

There are five colors available in each bag of Skittles. It is known that the 18% of the Skittles are red. On average, how many Skittles from a random sample of 40 (with replacement) would be expected to be red? Round to the nearest whole Skittle.

A)About 1
B)About 7
C)About 16
D)About 8.

Question 37

According to the manufacturer of the candy Skittles, 25% of the candy produced are green. If we take a random sample of 10 bags of Skittles, what is the probability that the proportion in our sample of green candies will be more than 25%? Which statement, if any, is true for the conditions to use the Central Limit Theorem?

A)The success/failure conditions may not be satisfied.
B)The sample size is small compared to the population.
C)Though not from a random sample, we can assume that the bags are representative of the population.
D)All of these statements are not true.

Question 38

A random sample of 950 adult television viewers showed that 48% planned to watch sporting event X. The margin of error is 4 percentage points with a 95% confidence level. Does the confidence interval support the claim that the majority of adult television viewers plan to watch sporting event X?

A)No; the confidence interval means that we are 95% confident that the population proportion of adult television viewers who plan to watch sporting event X is between 46% and 50%.
B)Yes; the confidence interval means that we are 95% confident that the population proportion of adult television viewers who plan to watch sporting event X is between 44% and 52%
Which includes 50%.
C)Yes; the confidence interval means that we are 95% confident that the population proportion of adult television viewers who plan to watch sporting event X is between 46% and 50%.
D)None of the statements are accurate.

Question 39

Suppose that in a recent poll of 900 adults between the ages of 35 and 45, 22% surveyed said they have thought about participating in an extreme sport such as bungee jumping. Find the 95% confidence interval for the proportion of adults ages 35 to 45 who have thought about participating in an extreme sport such as bungee jumping then choose the correct interpretation. (Round to the nearest tenth of a percent)

A)The population proportion of adults ages 35 to 45 who have thought about participating in an extreme sport is between 13.9% and 30.1%, with a confidence level of 95%.
B)There is a 95% chance that the population of adults ages 35 to 45 who have thought about participating in an extreme sport is between 13.9% and 30.1%.
C)There is a 95% chance that the population of adults ages 35 to 45 who have thought about participating in an extreme is between 19.3% and 24.7%.
D)The population proportion of adults ages 35 to 45 who have thought about participating in an extreme sport is between 19.3% and 24.7%, with a confidence level of 95%.

Question 40

Complete the statement by filling in the blank. When constructing a confidence interval, a larger sample size will _________ the margin of error and the confidence interval will be

A)Increase, narrower
B)Increase, wider.
C)Decrease; narrower.
D)Decrease, wider.

Question 41

Use the following information to answer questions (16)-(18). From a random sample of workers at a large
corporation you find that 58% of 200 went on a vacation last year away from home for at least a week.
An approximate 95% confidence interval is (0.50, 0.66). Which of the following statements is a correct interpretation?

A)95% of the coworkers fall in the interval (0.50, 0.66).
B)We are 95% confident that the proportion of coworkers who went on a vacation last year away from home for at least a week is between 50% and 66%.
C)There is a 95% chance that a random selected coworker has gone on a vacation last year away from home for at least a week.
D)We are 95% confident that between 50% and 66% of the samples will have a proportion near 58%.

Question 42

It is thought that 10% of all children have some level of nearsightedness. 200 randomly selected children, selected without replacement, had their eyesight tested. Can the Central Limit Theorem be used to find a good approximation of the probability that more than 15% of the children will be nearsighted? Which statement is not true?

A)All of the statements are not true.
B)Relative to the population, the sample is not large enough.
C)The sample does not need to be randomized since all children are likely to have vision problems.
D)

Question 43

A group of battery powered toys produced in a day at a factory has a defect rate of 0.5%. Suppose a quality inspector randomly inspects 200 of the toys. Complete the following statement: The quality inspector should expect ____defective toys, with an error of ____.

A)1; 5%
B)10; 5%
C)1; 0.5%
D)10; 0.5%

Question 44

Use the following information to answer questions (16)-(18). From a random sample of workers at a large
corporation you find that 58% of 200 went on a vacation last year away from home for at least a week.
What is the margin of error for the 95% confidence interval of (0.50, 0.66) of coworkers who went on a vacation last year away from home for at least a week?

A)0.08
B)0.16
C)0.58
D)0.04

Question 45

Complete the statement by filling in the blanks. When constructing a confidence interval, if the level of confidence increases, the margin of error must _____ and the confidence interval will be .

A)Decrease, narrower.
B)Decrease, wider.
C)Increase; narrower.
D)Increase; wider.

Question 46

If you use an instrument to measure 1 ml of water and do it 3 times, weighing the water each time, you get 0.751, 0.753, and 0.750 grams. One ml of water should weigh 1.0 grams. The measurements are _________.

A)accurate but not precise
B)precise but not accurate
C)both precise and accurate
D)neither precise nor accurate

Question 47

A survey investigates whether residents of a certain city support an educational tax increase. Which of the following statements are true?

A) The true proportion of "Yes" in the population is p.
B) The proportion of "Yes" in one sample of sizen will be close to p if the Central Limit Theorem conditions are satisfied.
C) The proportions of "Yes" in many samples of size n will be approximately normally distributed with mean =p and standard deviation equal to the square root of
D) All of the above.

Question 48

Complete the statement by filling in the blanks. A larger sample size will improve the precision of the confidence interval, therefore, assuming no other values change, the margin of error will _____ and the confidence interval will be _____.

A)Increase, wider.
B)Increase, narrower.
C)Decrease, wider.
D)Decrease; narrower.

Question 49

According to the manufacturer of the candy Skittles, 20% of the candy produced are red. If we take a random sample of 100 bags of Skittles, what is the probability that the proportion in our sample of red candies will be less than 20%? Which statement, if any, is not true for the conditions to use the Central Limit Theorem?

A)The success/failure conditions are satisfied.
B)The sample size is small compared to the population.
C)Though not from a random sample, we can assume that the bags are representative of the population.
D)All of these statements are true.

Question 50

Which of the following statements are characteristics of the sampling distribution of a sample proportion?

A)It is the probability distribution of a parameter.
B)It cannot be used for making inferences about a population.
C)The standard deviation of the sampling distribution is the same as the standard deviation of the population from which the data were sampled.
D)The mean of the sampling distribution is the same as the mean of the population from which the data were sampled.

Question 51

Which of the following statements is true about the confidence interval for a population proportion?

A)It is equal to the population proportion plus or minus a calculated amount called the standard error.
B)It is equal to the sample proportion plus or minus a calculated amount called the margin of error.
C)The confidence interval for a proportion will always contain the true population proportion.
D)The confidence interval for a proportion does not need a specified confidence level.

Question 52

The bias of is zero if certain conditions are met. Identify which condition is not required.

A)The sample is randomly selected from the population of interest.
B)The population must be at least 100 times bigger than the sample size.
C)The standard error of the sampling distribution is the same as the standard deviation of the population.
D)The mean of the sampling distribution is the mean of the population from which the data were sampled.

Question 53

Researchers are interested in learning more about the age of young adults who watch a certain television program. By interviewing people at a shopping mall, they can identify people who watch this show. The collection of the ages of these young adults who watch this television program is a _____________.

A)Population
B)Sample
C)Parameter
D)Statistic

Question 54

Use the following information to answer questions (16)-(18). From a random sample of workers at a large
corporation you find that 58% of 200 went on a vacation last year away from home for at least a week.
Which of the following statements are correct concerning the 95% confidence interval of (0.50, 0.66) of coworkers who went on a vacation last year away from home for at least a week?

A)If the sample size is 500 instead of 200, the confidence interval will be larger.
B)A maximum of 66% of the coworkers went on a vacation last year away from home for at least a week.
C)If the confidence level were changed from 95% to 99%, the confidence interval would become wider.
D)If the confidence level were changed from 95% to 90%, the confidence interval would become wider.

Question 55

A polling agency wants to compare support for the president's foreign policies between men and women. They surveyed 2500 U.S. citizens and found a 95% confidence interval for the difference in proportions between men and women who support the president's foreign policies as (-0.05 to -0.025) where population 1 is men and population 2 is women. Select the correct interpretation of this result.

A) The interval estimates that which shows that women are more likely than men to support with the president's fore1gn policies.
B) The interval estimates that which shows that men are more likely than women to support with the president's foreign policies.
C) The interval does not contain 0 , which shows that there is no significant difference in the proportions between men and women.
D) The number surveyed should be increased to increase the accuracy of the confidence interval.

Question 56

Is it plausible that more than 10% of Americans believe in aliens? A random sample of 2000 adult Americans were surveyed and 15% of them said that they believed in aliens. Find the 95% confidence interval for the proportion of Americans who believe in aliens then choose the correct interpretation. (Round to the nearest tenth of a percent)

A)The population proportion of Americans who believe in aliens is between 15% +/- 1.6% with a confidence level of 95%.The interval is higher than 10% and therefore, it is
Plausible that more than 10% of Americans believe in aliens.
B)The population proportion of Americans who believe in aliens is between 15% +/- 1.6% with a confidence level of 95%.The interval includes 10% and therefore, it is plausible
That at least 10% of Americans believe in aliens.
C)The population proportion of Americans who believe in aliens is between 10% +/- 1.6% with a confidence level of 95%.The interval includes 10% and therefore, it is plausible that at least
10% of Americans believe in aliens.
D)The population proportion of Americans who believe in aliens is between 15% +/- 0.8% with a confidence level of 95%.The interval does not include 10% and therefore, it is not plausible
That at least 10% of Americans believe in aliens.

Question 57

A survey recently reported that 35% of U.S. citizens believe that we never landed on the moon. The pertinent question in the survey was "Do you think it was possible or impossible that the event of the U.S. landing on the moon never happened?" Select the most accurate statement about this survey.

A)The question worded in a confusing way caused measurement bias.
B)The question worded in a confusing way caused sampling bias.
C)The question worded in a confusing way caused response bias.
D)The results are significant.