Name: Assignment 20: Goodness Of Fit Tests You should be able to do the first two problems without a calculator. 1. Six hospitals received 300 boxes of supplies from the federal government. As the hospitals were similar in size, they were expecting to each receive the same number of boxes. The number of boxes they actually received was as follows: General County Main Children's Critical Care Veteran's Total 51 46 52 53 45 53 300 (a) After discussions among the hospital administrators, they claim the shipments they received did not match what they expected. To test that claim, first complete this table of expected values: General County Main Children's Critical Care Veteran's | Total (b) Find and simplify the test statistic. (c) Use a significance level of o = 0.01 to test the hypothesis. Draw a picture showing the test statistic, critical values(s), and shading the critical region. What do you conclude? 2. Five hospitals also received some bottles of special medications from the federal government. The distribution of these was based on the numbers of doctors in various specialties. The expected and actual number of bottles each hospital received is summarized in the table below: General County Main Critical Care Veteran's Total expected 16 8 10 52 actual 12 12 16 52 (a) After discussions among the hospital administrators, they claim the shipments they received did not match what they expected. To test that claim, find and simplify the test statistic. (b) Use a significance level of o = 0.1 to test the hypothesis. Draw a picture showing the test statistic, critical values(s), and shading the critical region. What do you conclude?3. For this problem, you should show all computations in both fraction form, and also as a decimal rounded to 5 decimal places. The data below are actual numbers of deaths due to tuberculosis (TB) in 1910, in both New York City and Richmond, VA. They were reported on p. 449 of An Introduction to Logic and the Scientic Method by Cohen and Nagel, 1934. (a) In NYC, with population 4,766,383, there were 8,378 deaths due to TB. In Richmond, with population 127,663, there were 286 deaths due to TB. In which city was the rate of death due to TB lower? (b) When the populations of both cities are broken down into white and non-white residents, we get the following data: TB Deaths NYC Richmond white 8, 365 13 1 8496 nonwhite 513 155 663 837 3 286 9164 Total population NYC Richmond white 4, 675, 174 30, 895 4,756,069 nonwhite 91 , 709 46, 773- 138,482 4,766,833 127,668 4,394,551 Use both tables above to nd the rate of death due to TB in NYC for white residents (so you're nding a straight probability, the number of people who were white and died of TB in that city divided by the number of people who were white in that city). Then nd a similar rate for Richmond. Which is lower? Find the rate of death due to TB for in NYC for nonwhite residents, and a similar rate for Richmond. Which is lower? So if you were alive in 1910, and wanted to reduce your chances of getting TB, the results of question 1 would suggest you live in NYC, but the results of question 2 would suggest you live in Richmond This is puzzling. Give some thought to this, and we will revisit this problem when we can do goodness of t tests on contingency (twoway) tables