A random sample of 40 online retailers is selected to estimate the average price of a particular item.The average price in the sample is $1.38.Suppose you build a 99% confidence interval estimate of the average price of the item for the population of online retailers represented here.Suppose further that the interval turns out to be $1.38 ± $.20.How would you interpret your result?
A)The price of the item for 99% of all online retailers who sell the item will be between $1.18 and $1.58.
B)The price of the item for 99% of the online retailers in the sample is between $1.18 and $1.58.
C)We can be 99% confident that all online retailers who sell the item charge between $1.18 and $1.58 for the item.
D)We can be 99% confident that the interval $1.29 to $1.47 contains the average price of the item for the population of online retailers who sell the item.
E)We can be 99% confident that the interval $1.29 to $1.47 contains the average price of the item for the sample of online retailers we sampled.

Question

Quizplus · Accepted Answer

The correct interpretation of a confidence interval is about the population parameter (in this case, the average price of the item among all online retailers), not about the sample or individual observations. The interval $1.18 to $1.58 is the correct interval given, but the explanation in D correctly describes the confidence we have in where the true population mean lies, not the prices of individual retailers or the sample.

A Random Sample of 40 Online Retailers Is Selected to Estimate