Suppose that, for the population of UVA undergraduate and graduate students, the distribution of age has a mean of 23 and a standard deviation of 2 years. We take a simple random of size 100 from this population to survey their attitudes towards course enrollment. In this sample, the sample mean age is x ̅ = 22.5. of course, a different random sample of 100 UVA students would likely return a different sample mean age. What is the sampling distribution x ̅?
a. A Normal distribution with a mean of 22.5 and a standard deviation of 0.2
b. A Normal distribution with a mean of 22.5 and a standard deviation of 2
c. A Normal distribution with a mean of 23 and a standard deviation of 0.2
d. A Normal distribution with a mean of 23 and a standard deviation of 2
3 answers
c. A Normal distribution with a mean of 23 and a standard deviation of 0.2
why would the mean not be 22.5
The mean of the sampling distribution, denoted by μx̅, is equal to the population mean, which in this case is 23. The sample mean age of 22.5 is just one particular value obtained from a specific random sample, and it is likely to differ from the population mean. The sampling distribution, however, will have a mean equal to the population mean.
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