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Chapter 8: Q 21. (page 508)

California鈥檚 traffic People love living in California for many reasons, but traffic isn鈥檛 one of them. Based on a random sample of 572employed California adults, a 90%confidence interval for the average travel time to work for all employed California adults is 23minutes to 26 minutes.

a. Interpret the confidence level.

b. Name two things you could do to reduce the margin of error. What drawbacks do these actions have?

c. Describe how non response might lead to bias in this survey. Does the stated margin of error account for this possible bias?

Short Answer

Expert verified

a. 90%of all samples have 90%confidence interval that has correct average travel times.

b. It increases sample size and decreases confidence level.

c. It results after not having appropriate data for everybody.

Step by step solution

01

Given Information

Sample of 572California adults is given.

90%confidence interval is given.

Average time is23-26minutes.

02

Explaining Confidence Level

90%of all samples has 90% confidence interval that contain right average travel time for all employed adults of California.

03

Drawbacks of these Action

It decreases Margin of Error as:

  • Increase in Sample Size: It give more data about population and we obtain correct estimate. It is expensive and time consuming to collect data.
  • Decrease in Confidence Level: Confidence interval having correct population interval is less confident. It has less possible values for true population parameter. Hence, it is less confident about confidence interval having correct population parameter.
04

Non Response Bias

When there is not enough data for everybody in the sample, it results in non response bias. Persons whose data is not available results in overestimating or underestimating the true population and cause bias.

Margin of Error is not included here as it accounts for possible variation only.

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Most popular questions from this chapter

The Gallup Poll interviews 1600 people. Of these, 18% say that they jog regularly. The news report adds: 鈥淭he poll had a margin of error of plus or minus three percentage points at a 95% confidence level.鈥� You can safely conclude that

a. 95% of all Gallup Poll samples like this one give answers within 卤3% of the true population value.

b. the percent of the population who jog is certain to be between 15% and 21%.

c. 95% of the population jog between 15% and 21% of the time.

d. we can be 95% confident that the sample proportion is captured by the confidence interval.

e. if Gallup took many samples, 95% of them would find that 18% of the people in the sample jog.

The researcher is deciding between a 95% confidence level and a 99% confidence level. Compared with a 95% confidence interval, a 99% confidence interval will be

a. narrower and would involve a larger risk of being incorrect.

b. wider and would involve a smaller risk of being incorrect.

c. narrower and would involve a smaller risk of being incorrect.

d. wider and would involve a larger risk of being incorrect.

e. wider and would have the same risk of being incorrect.

Three branches According to a recent study by the Annenberg Foundation, only 36%of adults in the United States could name all three branches of government. This was based on a survey given to a random sample of1416U.S. adults.

a. Construct and interpret a 90%confidence interval for the proportion of all U.S. adults who could name all three branches of government.

b. Does the interval from part (a) provide convincing evidence that less than half of all U.S. adults could name all three branches of government? Explain your answer.

The 10%condition When constructing a confidence interval for a population proportion, we check that the sample size is less than 10%of the population size.

a. Why is it necessary to check this condition?

b. What happens to the capture rate if this condition is violated?

Explaining confidence A 95%confidence interval for the mean body mass index (BMI) of young American women is 26.8卤0.6. Discuss whether each of the following explanations is correct, based on that information.

a. We are confident that 95%of all young women have BMI between 26.2and 27.4.

b. We are 95%confident that future samples of young women will have mean BMI

between 26.2and27.4.

c. Any value from 26.2to27.4is believable as the true mean BMI of young American women.

d. If we take many samples, the population mean BMI will be between 26.2and 27.4in about 95%of those samples.

e. The mean BMI of young American women cannot be 28.
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