On January 24, 2000 the Holland Sentinel reported on a study that found the greater the hair loss on top of a man's head, the greater the risk for heart disease.  This study, co-authored by Dr. JoAnn Manson from Harvard's Brigham and Women's Hospital in Boston, analyzed baldness patterns of 22,000 male doctors who were 40 to 84 years old when enrolled in the Physician's Health Study.  Eleven years into the study, the researcher asked the doctors to describe their patterns of baldness at age 45.
 

1. In another study researchers selected a sample of 663 heart disease patients (male) and a control group of 772 males not suffering from heart disease. Each was asked to classify their degree of baldness on a 5-point scale. The results are given in the following table.  Use these data to answer the following questions.

1. Of those in the control group, what percent claimed to have:
1. Little or no baldness?
2. Some, much or extreme baldness?

2. Of those with heart disease, what percent claimed to have:
1. Little or no baldness?
2. Some, much or extreme baldness?

3. At this stage in the investigation, state whether you think there is a relationship between heart disease and baldness. Explain your answer.

4. We are now going to run a test of significance on this.
1. State the null and alternative hypotheses you would use to test whether there is a relationship between heart disease and baldness.
2. Complete a chi-square test to determine if there is a relationship between heart disease and baldness.  (Type the data into Minitab - you don't need any of the column or row headings, just the data.  Use Stat > Tables > Chi-square Test.)  Make sure you give the chi-square statistic, the P-value, and a conclusion.

5. Briefly discuss whether your results necessarily mean that heart disease is caused by baldness or baldness is caused by heart disease.

2. Another type of chi-square test is a goodness-of-fit test.  Instead of testing a two-way table for independence, this test can determine whether or not a sample is drawn from a specific sort of distribution.  For example, you can use a chi-square goodness-of-fit test to determine whether or not the colors of peanut m&m's are distributed evenly.  We will do an example similar to this, except we will use marbles.  Go to the Random Marble Grabber and grab 100 marbles.  This applet will give you a chi-square statistic based on the null hypothesis that the 10 colors are distributed evenly.  (You can find the P-value on Minitab by selecting Calc > Probability Distributions > Chi-Square.  In the window that pops up click on Cumulative Probability, leave 0.0 as the Noncentrality parameter, put in 9 for your Degrees of freedom, click on Input constant, input your chi-square statistic from the applet, and click OK.)  The value that Minitab gives you is one minus the P-value.  Write up the results from your test by including the hypotheses, the chi-square statistic, the P-value, and a conclusion.