this is statistics in psychology Sampling Distribution. A quarterback threw I in

Question

this is statistics in psychology

Sampling Distribution. A quarterback threw I interception in his first game, 2 interceptions in his second game, 5 in- terceptions in his third game, and then he retired. Consider the values of 1, 2, and 5 to be a population. Assume that samples of size 2 are randomly selected (with replacement) from the population. a. List the 9 different possible samples and find the mean of each sample. b. What is the mean of the sample means from part a? c. Is the mean of the sampling distribution from part b equal to the mean of the population of the three listed values? Are those means always equal?

Explanation / Answer

let first outcome is x1 and second outcome is x2:

below is table of sampling distirbution and their mean

:

b) mean of sample means =24/9=2.6667

c) mean of population =(1+2+5)/3 =2.6667

hence both are equal

Yes they are always equal.

x1 x2 mean 1 1 1 2 1 1.5 5 1 3 1 2 1.5 2 2 2 5 2 3.5 1 5 3 2 5 3.5 5 5 5 total 24

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