Question

# A pediatrician has three patients with measles and they are ages 2​, 4​, and 12. Assume...

A pediatrician has three patients with measles and they are ages 2​, 4​, and 12. Assume that samples of size nequals2 are randomly selected with replacement from the population. Listed below are the nine different samples. Complete parts​ (a) through​ (d) below.

2​,2 2​,4 2​,12 4​,2 4​,4 4​,12 12​,2 12​,4 12​,12

a. Find the value of the population standard deviation sigma.

sigma =

​(Round to three decimal places as​ needed.)

b. Find the standard deviation of each of the nine samples and then summarize the sampling distribution of the standard deviations in the format of a table representing the probability distribution.

c. Find the mean of the sampling distribution of the sample standard deviations. The mean of the sample standard deviations is the sum of the nine sample standard deviations divided by the number of samples.

d. Based on the preceding​ results, is the sample standard deviation an unbiased estimator of the population standard​ deviation? Why or why​ not?