Suppose three students conduct a group project to estimate the proportion of stu

Question

Suppose three students conduct a group project to estimate the proportion of students at their university who are from a different state. They take a random sample of students and find that 20% of their sample of students are from a different state. They then determine the following confidence intervals for the population proportion who are from a different state. One of these is a 90% confidence interval, one is a 99% confidence interval, and one is incorrect. Identify which is which. (In other words, write “90%” below the appropriate interval, “99%” below another, and “incorrect” below the third.) (.156, .244) (.196, .244) (.146, .254)

Explanation / Answer

Note that the confidence intervals should be centered at 0.20, as that is the best estimate.

Also, note that the widest would be the 99% interval, then the narrower is the 90%.

Hence:

(.156, .244) [Centered at 0.20, narrower. 90%]

(.196, .244) [Note centered at 0.20, INCORRECT]

(.146, .254) [Centered at 0.20, widest. Hence, 99%]

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