Inference

Instructions

Start a fresh page in your classwork notebook. Write today’s date in the margin of the page. Clearly label and solve each of the following. Show your work and circle the anwer.

Discussion Questions

1. 2012, Practice Exam, #10

A compact disc manufacturer wanted to determine which of two different cover designs for a newly released CD will generate more sales. The manufacturer chose 70 stores to sell the CD. Thirty-five of these stores were randomly assigned to sell CDs with one of the cover designs and the other 35 were assigned to sell the CDs with the other cover design. The manufacturer recorded the number of CDs sold at each of the stores and found a significant difference between the mean number of CDs sold for the two cover designs. Which of the following gives the conclusion that should be made based on the results and provides the best explanation for the conclusion?

1. It is not reasonable to conclude that the difference in sales was caused by the different cover designs because this was not an experiment.

2. It is not reasonable to conclude that the difference in sales was caused by the different cover designs because there was no control group for comparison.

3. It is not reasonable to conclude that the difference in sales was caused by the different cover designs because the 70 stores were not randomly chosen.

4. It is reasonable to conclude that the difference in sales was caused by the different cover designs because the cover designs were randomly assigned to stores.

5. It is reasonable to conclude that the difference in sales was caused by the different cover designs because the sample size was large.

2. 2009, Free Response Form B, #3

A French study was conducted in the 1990s to compare the effectiveness of using an instrument called a cardiopump with the effectiveness of using traditional cardiopulmonary resuscitation (CPR) in saving lives of heart attack victims. Heart attack patients in participating cities were treated with either a cardiopump or CPR, depending on whether the individual’s heart attack occurred on an even-numbered or an odd-numbered day of the month. Before the start of the study, a coin was tossed to determine which treatment, a cardiopump or CPR, was given on the even-numbered days. The other treatment was given on the odd-numbered days. In total, 754 patients were treated with a cardiopump, and 37 survived at least one year; while 746 patients were treated with CPR, and 15 survived at least one year.

1. The conditions for inference are satisfied in the study. State the conditions and indicate how they are satisfied.

2. Perform a statistical test to determine whether the survival rate for patients treated with a cardiopump is significantly higher than the survival rate for patients treated with CPR.

3. 2012, Free Response, #3

Independent random samples of 500 households were taken from a large metropolitan area in the United States for the years 1950 and 2000. Histograms of household size (number of people in a household) for the years are shown below.

1. Compare the distributions of household size in the metropolitan area for the years 1950 and 2000.

2. A researcher wants to use these data to construct a confidence interval to estimate the change in mean household size in the metropolitan area from the year 1950 to the year 2000. State the conditions for using a two-sample t-procedure, and explain whether the conditions for inference are met.