4. Sample data, sample size, the confidence level, and the confidence interval

Suppose you are a summer intern working with a team studying the automobile industry. In one phase of the investigation, you are helping to develop an interval estimate of the proportion of automobile parts suppliers that are unionized.

You and your teammate work with the same sample. Your teammate, who feels older and wiser, thinks that he can make a more conservative estimate if he chooses a lower confidence level than yours.

Think about plotting both your interval estimate and your teammate's interval estimate on a number line and then comparing their positions (where they sit) on the number line and their widths.

Which of the following statements best describes where the intervals sit on the number line? Be as specific as you can.

Your teammate's interval is centered at a higher value than yours.

They are centered at different values.

They are centered at the same value.

Your teammate's interval is centered at a lower value than yours.

Which of the following statements best describes the widths of the two intervals? Be as specific as you can.

They are not the same width.

Your teammate's interval is wider than yours.

They are the same width.

Your teammate's interval is narrower than yours.

Who is taking a bigger risk of being wrong?

You

Your teammate