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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

Election polling Gloria Chavez and Ronald Flynn are the candidates for mayor in a large city. We want to estimate the proportion p of all registered voters in the city who plan to vote for Chavez with 95%confidence and a margin of error no greater than 0.03. How large a random sample do we need?

Selling online According to a recent Pew Research Center report, many

American adults have made money by selling something online. In a random sample of 4579American adults, 914reported that they earned money by selling something online in the previous year. Assume the conditions for inference are met.

Determine the critical value z* for a 98% confidence interval for a proportion.

b. Construct a 98% confidence interval for the proportion of all American adults who

would report having earned money by selling something online in the previous year.

c. Interpret the interval from part (b).

Bone loss by nursing mothers Breast-feeding mothers secrete calcium into

their milk. Some of the calcium may come from their bones, so mothers may lose bone mineral. Researchers measured the percent change in bone mineral content (BMC) of the spines of 47randomly selected mothers during three months of breast-feeding. The mean change in BMC was −3.587%and the standard deviation was 2.506%

a. Construct and interpret a 99%confidence interval to estimate the mean percent change in BMC in the population of breast-feeding mothers.

b. Based on your interval from part (a), do these data give convincing evidence that

nursing mothers lose bone mineral, on average? Explain your answer.

After deciding on a 95% confidence level, the researcher is deciding between a sample of size n=500 and a sample of size n=1000. Compared with using a sample size of n=500, a confidence interval based on a sample size of n=1000 will be

a. narrower and would involve a larger risk of being incorrect.

b. wider and would involve a smaller risk of being incorrect.

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

d. wider and would involve a larger risk of being incorrect.

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

Gambling and the NCAA Gambling is an issue of great concern to those involved in college athletics. Because of this concern, the National Collegiate Athletic Association (NCAA) surveyed randomly selected student athletes concerning their gambling-related behaviors. Of the 5594Division Imale athletes who responded to the survey, 3547reported participation in some gambling behavior. This includes playing cards, betting on games of skill, buying lottery tickets, betting on sports, and similar activities. A report of this study cited a 1%margin of error.

a. The confidence level was not stated in the report. Use what you have learned to

estimate the confidence level, assuming that the NCAA took an SRS.

b. The study was designed to protect the anonymity of the student athletes who responded. As a result, it was not possible to calculate the number of students who were asked to respond but did not. How does this fact affect the way that you interpret the results?
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