19. Sampling Distribution. A quarterback threw 1 interception in his first game,

Question

19. Sampling Distribution. A quarterback threw 1 interception in his first game, 2 interceptions in his second game, Sinterceptions in his third game, and then he retired. Consider the values of I, 2, and 5 to be a population. Assume thatsamples of size 2 are randomly selected (with replacement) from the population List the 9 different possible samples and find the mean of each sample. a. Answer:Complete the following chart to help you answer part a of the question Samples 1,1 Sample Mean b. What is the mean of the sample means from part a? Answer: The mean of the sample in part a - e.ls 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? Answer:The mean of the population iswhich is the [possible answers: the same or different] as the mean of the sample means in part (a). Therefore, these means [possible answers: will OR will not] always be equal.

Explanation / Answer

Different possible samples when picked two elements out of {1,2,5} with replacement:

a.

b. Mean of sample means = (1+2+5+1.5+3+1.5+3.5+3+3.5)/9

= 24/9

= 2.667

c. Mean of population = (1+2+5)/3 = 2.667

Answer: The mean of population is 2.667, which is same as the mean of sample means in (a).

Therefore, these means will always be equal.

Samples 1,1 2,2 5,5 1,2 1,5 2,1 2,5 5,1 5,2 Sample Mean 1 2 5 1.5 3 1.5 3.5 3 3.5

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