statistic worksheet

Neatly respond to each prompt. Show all work for full credit. Round to four decimal places.

1. Let X1, X2, … Xn be a random sample from a population and let E(Xi) = μ and Var(Xi) = σ2.

a. Identify an unbiased estimator other than , show that it is unbiased, and find its variance.

b. Show that is an unbiased estimator of μ and find its variance.

c. In general, will your estimator or be a better estimator for μ? Use your work in a and b to justify your response.

3. Why do we report a standard error along with a point estimate? What additional information does the standard error give us about the estimate?

4. What is the sampling distribution of a statistic? Explain in your own words.

5. For each scenario below, identify the parameter of interest by name and by symbol, state which statistic would be used to estimate the parameter (again, by name and by symbol). Identify the value of the parameter and statistic where possible.

a. Researchers hope to estimate the false positive rate of a medical screening test for a particular illness. To this end, they examine 324 positive results. They find that 23 of these were false positives.

b. Measurements are made of the total daily natural gas consumption for a region for both the summer time and the winter time. Researchers would like to know if the mean natural gas consumption varies between winter and summer.