For a population of five individuals, television ownership is as follows:
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X = Number of Television sets owned
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Allen
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2
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Betty
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1
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Chuck
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3
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Dave
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4
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Eddie
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2
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a. Determine the probability distribution for the discrete random variable, x = number of television sets owned. Calculate the population mean and standard deviation.
b. For the sample size n = 2, determine the mean for each possible simple random sample from the five individuals.
c. For each simple random sample identified in part (b), what is the probability that this particular sample will be selected?
d. Combining the results of parts (b) and (c), describe the sampling distribution of the mean.
e. Repeat parts (b)-(d) using n = 3 instead of n = 2. What effect does the larger sample size have on the mean of the sampling distribution? On the standard error of the sampling distribution?