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Chapter 8: Q.52 (page 498)

I collect an SRS of size n from a population and compute a 95%confidence interval for the population proportion. Which of the following would produce a new confidence interval with larger width (larger margin of error) based on these same data?

(a) Use a larger confidence level.

(b) Use a smaller confidence level.

(c) Increase the sample size.

(d) Use the same confidence level, but compute the interval n times. Approximately5% of these intervals will be larger.

(e) Nothing can guarantee absolutely that you will get a larger interval. One can only say that the chance of obtaining a larger interval is 0.05.

Short Answer

Expert verified

Correct answer is (a) Use a larger confidence level

Step by step solution

01

Given information

Given in the question that, I collect an SRS of size nfrom a population and compute a 95%confidence interval for the population proportion .

02

Explanation

(a) A larger confidence level leads to better accuracy and thus the confidence interval will becomes wider.

(b) A smaller confidence level will decrease the accuracy and thus lessen the width of the confidence interval.

(c) Increasing the sample size increases the accuracy and thus the width of the confidence interval decreases.

(d) This method does not lead to ONE larger confidence interval.

(e) Incorrect, because (a) is a valid method to obtain a larger interval.

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Most popular questions from this chapter

62. Blink When two lights close together blink alternately, we “see” one light moving back and forth if the time between blinks is short. What is the
longest interval of time between blinks that preserves the illusion of motion? Ask subjects to turn a knob that slows the blinking until they “see” two lights rather than one light moving. A report gives the results in the form “mean plus or minus the standard error of the mean.” Data for 12 subjects are summarized as 251±45 (in milliseconds).
(a) Find the sample standard deviation sx for these measurements. Show your work.
(b) Explain why the interval 251±45 is not a confidence interval.

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Engine parts Here are measurements (in millimeters) of a critical dimension on an SRS of 16of the more than 200auto engine crankshafts produced in one day:

224.120, 224.001, 224.017,223.982,223.989,223.960,224.089,223.987,223.976,223.902,223.980,224.098,224.057,223.913,223.999

(a) Construct and interpret a 95%confidence interval for the process mean at the time these crankshafts were produced.

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

- Determine the sample size required to obtain a level Cconfidence interval for a population mean with a specified margin of error.

Good wood? A lab supply company sells pieces of Douglas fir 4inches long and 1.5inches square for force experiments in science classes. From experience, the strength of these pieces of wood follows a Normal distribution with standard deviation 3000pounds. You want to estimate the mean load needed to pull apart these pieces of wood to within 1000pounds with 95%confidence. How large a sample is needed? Show your work.

- Understand how the margin of error of a confidence interval changes with the sample size and the level of confidence C.

High tuition costs Glenn wonders what proportion of the students at his school think that tuition is too high. He interviews an SRS of 50 of the 2400 students at his college. Thirty-eight of those interviewed think tuition is too high.
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