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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

America鈥檚 favorite cookie Ann and Tori wanted to estimate the average weight of an Oreo cookie to determine if it was less than advertised (34 grams for 3 cookies). They selected a random sample of 36cookies and found the weight of each cookie (in grams). The mean weight was x虅=11.3921grams with a standard deviation of sX=0.0817grams. Construct and interpret a 90%confidence interval for the true mean weight of an Oreo cookie.

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.

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

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

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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.

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