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Miami's car colorsUsing a webcam, a traffic analyst selected a random sample of 800cars traveling on I-195in Miami on a weekday morning. Among the 800cars in the sample, 24%were white. The margin of error for this estimate is 3.0percentage points.

a. Would you be surprised if a census revealed that 26%of cars onI-195 in Miami on a weekday morning were white? Explain your answer.

b. Explain how the traffic analyst could decrease the margin of error.

Short Answer

Expert verified

a. No, I would not be surprised if a census revealed that 26%of cars on I-195in Miami on a weekday morning were white.

b. Increasingthe sample size means increasing the number of cars traveling on I-195in Miami on a weekday morning, which will decrease the margins of error.

Step by step solution

01

Part (a) Step 1: Given Information

We are given following information:

The total number of random samples of cars is 800.

Total number of white cars out of 800= 24×800100=192

We need to explain will we be surprised if a census revealed that 26%of cars on I-195in Miami on a weekday morning were white.

02

Part (b) Step 2: Explanation

No, I would not be surprised if a census revealed that 26%of cars onI-195in Miami on a weekday morning were white because we expect that the parameters fall within the range of 27%to 21%.

Our data means that 26%of cars onI-195 in Miami on weekday mornings fall within our expected range.

03

Part (b) Step 1: Given Information

The total number of random samples of cars is 800.

The total number of white cars out of 800= 192.

The margin of error for this estimate is 3.0percentage points.

We need to explain decrease of margin due to traffic analyst.

04

Part (b) Step 2: Explanation

Increasing the sample size means increasing the number of cars traveling on I-195in Miami on a weekday morning, which will decrease the margins of error. With increasing the sample size, variability will get reduced, and we can get an accurate result.

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Most popular questions from this chapter

A local news agency conducted a survey about unemployment by randomly dialing phone

numbers during the work day until it gathered responses from 1000 adults in its state. In

the survey, 19% of those who responded said they were not currently employed. In reality,

only 6% of the adults in the state were not currently employed at the time of the survey.

Which of the following best explains the difference in the two percentages?

a. The difference is due to sampling variability. We shouldn’t expect the results of a

random sample to match the truth about the population every time.

b. The difference is due to response bias. Adults who are employed are likely to lie and

say that they are unemployed.

c. The difference is due to undercoverage bias. The survey included only adults and did

not include teenagers who are eligible to work.

d. The difference is due to nonresponse bias. Adults who are employed are less likely to

be available for the sample than adults who are unemployed.

e. The difference is due to voluntary response. Adults are able to volunteer as a member

of the sample.

In the experiment of the preceding exercise, the subjects were randomly assigned to the

different treatments. What is the most important reason for this random assignment?

a. Random assignment eliminates the effects of other variables such as stress and body

weight.

b. Random assignment is a good way to create groups of subjects that are roughly

equivalent at the beginning of the experiment.

c. Random assignment makes it possible to make a conclusion about all men.

d. Random assignment reduces the amount of variation in blood pressure.

e. Random assignment prevents the placebo effect from ruining the results of the study.

A report in a medical journal notes that the risk of developing Alzheimer’s disease among subjects who regularly opted to take the drug ibuprofen was about half the risk of those who did not. Is this good evidence that ibuprofen is effective in preventing Alzheimer’s disease?

a. Yes, because the study was a randomized, comparative experiment.

b. No, because the effect of ibuprofen is confounded with the placebo effect.

c. Yes, because the results were published in a reputable professional journal.

d. No, because this is an observational study. An experiment would be needed to confirm

(or not confirm) the observed effect.

e. Yes, because a 50%reduction can’t happen just by chance.

Apartment living You are planning a report on apartment living in a college town. You decide to select three apartment complexes at random for in-depth interviews with residents.

a. Explain how you would use a line of Table D to choose an SRS of 3complexes from the following list.

b. Use line 117to select the sample. Show how you use each of the digits.

iPhonesSuppose 1000iPhones are produced at a factory today. Management would like to ensure that the phones’ display screens meet their quality standards before shipping them to retail stores. Because it takes about 10minutes to inspect an individual phone’s display screen, managers decide to inspect a sample of 20phones from the day’s production.

a. Explain why it would be difficult for managers to inspect an SRS of 20iPhones that are produced today.

b. An eager employee suggests that it would be easy to inspect the last 20iPhones that were produced today. Why isn’t this a good idea?

c. Another employee recommends a different sampling method: Randomly choose one of the first50 iPhones produced. Inspect that phone and every fiftieth iPhone produced afterward. (This method is known as systematic random sampling.) Explain carefully why this sampling method is not an SRS.

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