Four randomly selected households are surveyed as a pilot project for a larger survey to be conducted later. The numbers of people in
the households are any four numbers of your choice between 10 and
20. Consider those values chosen to be a population. Assume that
samples of size n = 2 are randomly selected with replacement from
the population of the values you chose. Design a table with all the
possibilities.
A) (i) Find the median of each of the samples, then summarize the
sampling distribution of the medians in the format of a table
representing the probability distribution. (ii) Compare the
population median to the mean of the sample medians. (iii) Do
the sample medians target the value of the population median?
In general, do medians make good estimators of population
median? Why or why not?
B) (i) Find the variance of each of the samples, then summarize
the sampling distribution of the variances in the format of a
table representing the probability distribution. (ii) Compare
the population variance to the mean of the sample variances.
(iii) Do the sample variances target the value of the population
variance? In general, do variances make good estimators of
population variances? Why or why not?