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Chapter 8: Q 19. (page 508)

Prayer in school Refer to Exercise 5.

a. Explain what would happen to the length of the interval if the confidence level were increased to 99%.

b. How would a 95%confidence interval based on double the sample size compare to the original 95%interval?

c. The news article goes on to say: 鈥淭he theoretical errors do not take into account

additional errors resulting from the various practical difficulties in taking any survey of public opinion.鈥� List some of the 鈥減ractical difficulties鈥� that may cause errors which are not included in the 卤3 percentage point margin of error.

Short Answer

Expert verified

a. The length of interval increases.

b. On basis of double the sample size, confidence interval is narrower than original confidence interval.

c. It is not accountable for errors made during date of sample collection.

Step by step solution

01

Given Information

Confidence levels of95%,99%are given.

02

a. To explain effect on length of interval

If confidence level increases from 95%to99%, confidence that interval is having true parameter of population increases.

It has more possible values of true population parameter.

Hence, length of interval increases.

03

b. To explain how would a 95%confidence interval based on double the sample size compare to the original 95% interval.

Sample size increases when sample size is doubled. Hence, it will have more data about population and more correct estimates would be obtained.

Estimates would be more close to true value.

Hence., confidence interval needs to be narrower.

04

c. To determine that not included in ±3 percent point margin of error.

Margin of error contains possible variations only. It is not responsible for the errors made while collecting sample date.

Possible bias are:

  • Selection will exclude portion of population.
  • Response bias will use procedure showing values different from correct value.
  • Not containing data for everybody will cause no response bias.

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Most popular questions from this chapter

Losing weight A Gallup poll asked a random sample of U.S. adults, 鈥淲ould you like to lose weight?鈥� Based on this poll, the 95%confidence interval for the population

proportion who want to lose weight is (0.56,0.62).

a. Interpret the confidence interval.

b. What is the point estimate that was used to create the interval? What is the margin of error?

c. Based on this poll, Gallup claims that more than half of U.S. adults want to lose weight. Use the confidence interval to evaluate this claim.

Travel time to work A study of commuting times reports the travel times to work of a random sample of 20employed adults in New York State. The mean is x炉=31.25minutes and the standard deviation is sX=21.88

minutes. What is the standard error of the mean? Interpret this value in context.

A 90%confidence interval for the mean 渭 of a population is computed from a random sample and is found to be90卤30. Which of the following could be the 95%confidence interval based on the same data?

a. 90卤21

b. 90卤30

c. 90卤39

d. 90卤70

e. Without knowing the sample size, any of the above answers could be the 95%confidence interval.

Engine parts A random sample of 16 of the more than 200auto engine crankshafts produced in one day was selected. Here are measurements (in millimeters) of a critical component on these crankshafts:

a. Construct and interpret a 95%confidence interval for the mean length of this component on all the crankshafts produced on that day.

b. The mean length is supposed to be 渭=224mm but can drift away from this target during production. Does your interval from part (a) suggest that the mean has drifted from 224mm? Explain your answer.

Losing weight Refer to Exercise 6.

a. Explain what would happen to the length of the interval if the confidence level was decreased to 90%.

b. How would a 95%confidence interval based on triple the sample size compare to the original 95%interval?

c. As Gallup indicates, the 3percentage point margin of error for this poll includes only sampling variability (what they call 鈥渟ampling error鈥�). What other potential sources of error (Gallup calls these 鈥渘on sampling errors鈥�) could affect the accuracy of the 95% confidence interval?
See all solutions

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