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Chapter 8: Q. R8.8 (page 548)

It’s about ME Explain how each of the following would affect the margin of error of a confidence interval, if all other things remained the same.

a. Increasing the confidence level

b. Quadrupling the sample size

Short Answer

Expert verified

Part a) It could be said that an increase in the confidence level would lead increase in the margin of error.

Part b) it could be said that quadrupling the sample size would lead reduction in the margin of error.

Step by step solution

01

Part a) Step 1: Given information

All other things have remained constant.

02

Part a) Step 2: The objective is to explain the effect of the increase in the confidence level on the margin of error.

The margin of error is proportional to the confidence level, which means that an increase in confidence tends to increase the margin of error and vice versa.

Therefore, it could be said that an increase in the confidence level would lead increase in the margin of error.

03

Part b) Step 1: The objective is to explain the effect of quadrupling the sample size on the margin of error.

The margin of error is inversely proportional to the confidence level, which means that increasing the sample size reduces the margin of error and vice versa.

Therefore, it could be said that quadrupling the sample size would lead reduction in the margin of error.

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Most popular questions from this chapter

Student body totals Use your interval from Exercise 40 to construct and interpret a 99%confidence interval for the total number of students at the school that the student body president can identify by name. Then use your interval to evaluate the president’s claim.

Running red lights A random digit dialing telephone survey of 880 drivers asked, “Recalling the last ten traffic lights you drove through, how many of them were red when you entered the intersections?” Of the 880 respondents, 171 admitted that at least one light had been red.37

a. Construct and interpret a 95% confidence interval for the population proportion.

b. Nonresponse is a practical problem for this survey—only 21.6% of calls that reached a live person were completed. Another practical problem is that people may not give truthful answers. What is the likely direction of the bias: Do you think more or fewer than 171 of the 880 respondents really ran a red light? Why? Are these sources of bias included in the margin of error?

Good wood? A lab supply company sells pieces of Douglas fir 4 inches long and

1.5 inches square for force experiments in science classes. From experience, the strength of these pieces of wood follows a distribution with standard deviation 3000 pounds. You want to estimate the mean load needed to pull apart these pieces of wood to within 1000 pounds with 95% confidence. How large a sample is needed?

How confident? The figure shows the result of taking 25SRSs from a Normal population and constructing a confidence interval for the population mean using each sample. Which confidence level—role="math" localid="1654197644211" 80%,90%,95%,or99%—do you think was used? Explain your reasoning.

Age and September 11 Refer to Exercise 42. The study also reported that 86% of

millennials included 9/11 in their top-10 list and 70% of baby boomers included 9/11.

a. Explain why you do not have enough information to give confidence intervals for

millennials and baby boomers separately.

b. Do you think a 95%confidence interval for baby boomers would have a larger or smaller margin of error than the estimate from Exercise 42? Explain your answer.
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