Discussion Session Chapters 8 updated (2)

1 In-Class Activity: Chapter 8 Student N ame:____________________ SID:_________________ Section:___ CHAPTER 8 SECTION 8.1 8.1.1* Which of the following are true about the MAD statistic? There may be more than one statement that is true. A. The MAD statistic can never be negative. B. The MAD statistic is the average distance sample proportions are from each other. C. The MAD statistic is the average of a group of sample proportions. D. A MAD statistic of zero means that all the proportions are the same distance apart. E. As the MAD statistic increases, the p-value decreases. Giving blood and political party* Republican Democrat Independent Total Agree with a new law? Yes 125 201 178 504 N o 233 156 184 573 Total 358 357 362 1,077 EXERCISE 8.1.8 8.1.9 Suppose that you want to compare proportions of registered Democrats, Independents, and Republicans who have donated blood within the past year. 1. Which would be appropriate for this study: random sampling, random assignment, both, or neither? Explain. 2. If you find that the sample proportions who have donated blood are 0.20, 0.15, and 0.12, what more information would you need to determine if these proportions differ significantly? Sex and phone type* 8.1.11 Suppose 100 students are asked if the cellphone they use is a smartphone or a basic phone and the 8.1.11 two-way table summarizes the results. Male Female Total Smartphone 25 30 55 Basic phone 25 20 45 Total 50 50 100 EXERCISE 8.1.11 Courtney Machler 805 752 072 2D Random sample is 1 important to avoid Random sample because you're taking a sample but you're assigning bias people to a party whether or not they can donateblood The sample sizefrom each group the number of Democrats Republicans and Independents that are in the sample

2 1. Find the proportion of males that own smartphones and the proportion of females that own smartphones. 2. Determine the MAD statistic. 3. When comparing two proportions, you could use the difference in the proportions or the MAD as the statistic. How do these two statistics compare in this example? Will they always have the same relationship as in this example? Explain. 4. Put the data from the table in the Multiple Proportions applet and make null distributions using both the difference in proportions and the MAD statistic. Describe how these distributions are different. 5. Based on your answer from part (c), explain why a distribution of MAD statistics is skewed right when the distribution of differences in proportions is bell-shaped. Heart disease and baldness* 8.1.15 Many studies have been done to look at the relationship between heart disease and baldness. In one study, researchers selected a sample of 663 heart disease male patients and a control group of 772 male patients not suffering from heart disease from hospitals in eastern Massachusetts and Rhode Island. Each was asked to classify their degree of baldness. The results are given in the following table. Use these data to answer the following questions. EXERCISE 8.1.14 Baldness N one Little Some Much Total Heart disease Yes 251 165 195 52 663 N o 331 221 185 35 772 Total 582 386 380 87 1,435 Notice the degree of baldness uses ordered categories. This makes it possible to reduce the 2 × 42 × 4 table to a simpler one: 1. Of those in the control group, what percent claimed to have: i. Little or no baldness? ii. Some or much baldness? 2. Of those with heart disease, what percent claimed to have: i. Little or no baldness? ii. Some or much baldness? 3. At this stage in the investigation, state whether you think there is a relationship between heart disease and baldness. Explain your answer. We are now going to run a test of significance on these data using all four degrees of baldness. Use the data set HeartDiseaseAndBaldness . Males with smartphones 25 50 0.5 Females with smartphones 3 0.6 10.6 0.51 1 0.10 Inthis example the MAD is the absolute value of the diff in proportions because there is only 1 comparison happening not multiple with thediff in proportions you get a bell shaped distribution with a two sided p valof0.42 For the MAD stat you get a right skewed distribution but w the same p value Null distributions of Mean group diff are skewed right because the values are closer to o whereas the other is bell shaped because it's centered normally around a specific value 2214,31 35,51 9 715 71.5 y 0 285 28.51 1656631 0.627 62.71 52 66195 0.373 37.31 I think there is a correlation between heart disease baldness because the difference in proportions withthe control group suggests they are dependent on eachother Baldness appears to be more common among individual with heart disease

4 4. Identify the explanatory and response variables. Also, for each variable, identify whether it is categorical or quantitative. 5. State the appropriate null and alternative hypotheses in words . 6. Explain why it would NOT be okay to use the theory-based method to find a p-value for this study. 7. Describe how one might use everyday items (for example, coins, dice, cards, etc.) to conduct a tactile simulation-based test of the hypotheses. Be sure to clearly describe how the p-value will be computed from the simulation. 8. Use an appropriate applet (for example, the Multiple Proportions applet) to find and report the following from the data: (i) the name of a statistic and its numeric value and (ii) the simulation-based p-value. 9. Interpret the p-value in the context of the study. 10. State a complete conclusion about this study, including significance, causation, and generalization. Be sure to explain how you are arriving at your conclusion. Response whether or not the subject relapsed is i Null There isn't an association between type of medicine and Iternative there is an associationbetween type of medicine relapsing thepatient relapsing There are some groups with less than 10 in the sample so it wouldn't be valid If you got 48 pennies and 24 dimes you could shake y mix them together then separate into 3 even piles of 24 then find the chi square i Chi square 10.5 ii p value 0.005 we have strong evidence that there is an association between type of medicine relapse The chance of getting a chi square of 10.5 or greater assuming the null is true would be 0.00s There is strong evidence of a correlation between type of medicine possibility of relapsing since we used random assignment this would be causation cause and effect We probably can't generalize the results due to the little data we have on the participants Desipramine Lithium Carbonate Placebo Total 10 18 20 48 Relapse No relapse 14 6 4 24 Total 24 24 24 72