Sample data, sample size, the confidence level, and the confidence interval You

Question

Sample data, sample size, the confidence level, and the confidence interval You are a member of a team studying the automobile industry. One phase of your investigation is to develop an interval estimate of the average distance that automobile-parts suppliers are located from Detroit. The population standard deviation o is known. You select a random sample, your teammate selects her own random sample to be the same size as yours, and you both choose the same confidence level. Think about plotting both your interval estimate and your teammate's interval estimate on a number line and then comparing where they sit and their widths. Being as specific as you can, which of the following statements best describes where the intervals sit on the number line? Your teammate's interval is centered at a higher value than yours. Your teammate's interval is centered at a lower value than yours. They are centered at different values. They are centered at the same value. Being as specific as you can, which of the following statements best describes the widths of the two intervals? Your teammate's interval is wider than yours. They are not the same width. They are the same width. Your teammate's interval is narrower than yours.

Explanation / Answer

a)

We cannot say which one's center is higher, but we can be almost sure that they have a difference center, as they would probably have a different sample mean.

Hence,

OPTION C: They are centered at different values. [ANSWER]

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b)

Although we choose the same sample size and confidence level, the sample standard deviation also varies from sample to sample. Hence, we will have different widths,

OPTION B: They are not the same width. [ANSWER]

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