Question

1. A school superintendent wishes to estimate the mean number of children per family in her school district. She takes a simple random sample of 500 students in the district and asks them, “How many children are there in your family, including yourself?” All 500 students respond and the mean response is 2.7 children. Is 2.7 a reasonable estimate of the mean number of children per family in the district? Answer yes or no and explain. (Hint: consider observational units.)

Answer 1

NO, 2.7 a reasonable estimate of the mean number of children per family in the district.

Here the observational unit is the number of children. It is not some quantity like weight or height which can be in decimals.

The number of children per family in can only be positive integer. So the average of 2.7 children does not convey any valid meaning. There cannot be 2.7 children, it does not make any sense. The number of children should thus be rounded off to the closest integer which is 3 in order to draw valid conclusion from the random sampling method.