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

It鈥檚 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

Food fight A 2016survey of 1480randomly selected U.S. adults found that 55%of respondents agreed with the following statement: 鈥淥rganic produce is better for health than conventionally grown produce.鈥�

a. Construct and interpret a 99%confidence interval for the proportion of all U.S. adults who think that organic produce is better for health than conventionally grown produce.

b. Does the interval from part (a) provide convincing evidence that a majority of all U.S. adults think that organic produce is better for health? Explain your answer.

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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

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

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

Can you taste PTC? PTC is a substance that has a strong bitter taste for some people and is tasteless for others. The ability to taste PTC is inherited. About 75%of Italians can taste PTC, for example. You want to estimate the proportion of Americans who have at least one Italian grandparent and who can taste PTC.

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