Based on the Law of Large Numbers we know that any sample va

Based on the Law of Large Numbers, we know that any sample value will tend to lie closer and closer to the thrue population value (parameter: p or u) as the sample size becomes larger and larger. Therefore, a larger sample size will yeild a histogram of sample statisic values that are closer to the populatin parameter than will a smaller size. With this in mind anser the following question.

The average monthly cell phone bill (the parameter) for a particular carrier in Pittsburgh, PA is $90. Which of the following is most likley?

A) The average monthly cell phone bill (a statistic) for 50 randomly selected customers (of this carrier) is over $115.

B)The average monthly cell phone bill (a statistic) for for 250 randomly selected customers (of this carrier) is over $115.

C) Both A nd B are equally likely

Solution

From the law of large numbers

A)The average monthly cell phone bill (a statistic) for 50 randomly selected customers is over $115 is most likely

Because as the sample size increases the average phone bill will come more closer to mean ($90) so for 250 sample size is least likely possible to have bill >115 than with 50 sample size