Question

Assume we have a box with 10 chips, each with a number written on it from 1-10. Consider this to be our population of scores.

We reach in, pull out a chip, look at the number and write it down, then put the chip back. We do
this 2 times. We describe this as N = 2 for the sample size. Then we take the mean of the two numbers
we recorded. Which values for the mean are least likely to occur? Which value is most likely? Why?

Answer 1

The probability of drawing a chip in the first draw i.e., N=1 is 1/10.

Since we put the chip back after it is drawn ,the probability of drawing a chip in the second draw i.e., N=2 will be 1/10.

Hence each chip has equal probability to get picked in both the draws. The minimum value on the chip can be 1 and the maximum value on the chip can be 10.

Therefore the mean of the two numbers cannot be less than 1 and also cannot be more than 10.

The mean can have values from 1 to 10 with each having equal probability.