1. The Great M&M’s Mystery! Section 13.1.1

2. Starter 13.1.1 Sickle-cell trait is a hereditary condition that is common among blacks and can cause medical problems. Some biologists suggest that the trait protects against malaria. A study in Africa tested 543 children for the sickle-cell trait and also for malaria. In all, 136 of the children had the sickle-cell trait, and 36 of these had heavy malaria infections. The other 407 children lacked the trait, and 152 of them had heavy malaria infections. 1.What are the two populations of interest here? 2.Give a 95% Confidence Interval for the difference in proportions of malaria in the two populations. 3.Is there good evidence that the proportion of heavy malaria infection is lower among children with the sickle-cell trait?

3. Today’s Objectives Students will sample a population and write the distribution of a categorical variable. California Standard 19.0 Students are familiar with the chi- square distributions and chi- square test and understand their uses.

4. The Big Picture (so far) Chapter 11: Estimating means –One population: μ = some constant –Two populations: μ 1 = μ 2 Chapter 12: Estimating proportions –One population: p = some percent –Two populations: p 1 = p 2 Chapter 13: Comparing distributions –We will now consider categorical variables with more than 2 outcomes. –Is a sample significantly different from population?

5. Activity Scoop a cup of M&M’s from the barrel. Record the counts of each color in this order: Brown, Yellow, Red, Blue, Orange, Green. Come to the front of the room and report your counts to me in that order. Add the class totals for each color to your paper. Calculate the relative frequency of each color and add them to your paper.

6. Activity Continued From the M&M's website find the theoretical distribution of colors.M&M's website –Add those relative frequencies to your chart. Calculate how many of each color you would have expected the class to find based on the M&M version of the distribution. –Add those expected counts to your chart.

7. Activity Conclusion Draw a bar graph that shows both distributions. –Use one graph with paired bars for each color. –Let vertical axis represent percents. –(Why is this not a histogram?) Write a comment describing how well the distribution we found agrees with the distribution we expected. Save these results for use tomorrow.

8. Today’s Objectives Students will sample a population and write the distribution of a categorical variable California Standard 19.0 Students are familiar with the chi- square distributions and chi- square test and understand their uses.

9. Homework Read pages 700 – 701 Do Activity 13 problems 2 - 5