Lab 13 for Math 17 - Chi-square Investigations + Name that Scenario

Lab 1b for Math 17: Curious Cookie Questions 1 Cookie Introduction The Keebler elves have recently grown concerned about cookie consumption of Chips Ahoy compared to their own brand. To investigate the possible causes for why consumers may be swapping to Chips Ahoy and improve their own cookie brand consumption, they have hired you (the class) and given you a five dollar expense account, which has been spent on a carton of Keebler cookies and napkins. Future expenses may allow for the purchase of Chips Ahoy brand cookies. As the hired statistician, with your consulting group, it is your job to tell the elves what they can do to improve their cookies in relation to Chips Ahoy. One of the first things you must do is determine what characteristics make a good cookie and that you can measure in order to compare cookies. 1. What characteristics do you think make a good cookie? 2. Can you measure those characteristics? How? 3. Are there any characteristics that you cannot measure or that might result in subjective measurements? 4. What are some possible sources of variability in the measurements you are thinking about? The characteristics you have listed are variables related to cookies. In this case, for each cookie you examine, you might determine if the cookie is a good cookie and record a 0 for the cookie if it is not good and a 1 if it is good. You might name that variable “good cookie” - in which case it would be a categorical response variable with a numerical coding. 5. Most of the characteristics you listed above are explanatory / response variables (choose one). 6. What is an example quantitative (numerical) variable you listed? 7. What is a basic plot that could be used to display that quantitative variable? (Hint: We have not discussed it in depth yet.) 1 2 Data Collection The next issue you need to address is how to collect data about the cookies. Obviously, since you only have one carton of cookies, all your measurements must come from that carton (for now). Now, you may have learned about some issues about gathering data this way, but for now, let’s focus on data collection. Imagine that after brainstorming all sorts of cookie characteristics to measure, the chief elf (his name is Ernie) has just told you that he thinks the cookie issue may depend on the amount of chocolate chips in the cookies. Since you have no scale, you’ll need to simply count the number of chips in your cookie (as best you can), and assemble a data set with the class (one measurement per person). However, there’s one more issue... how should you distribute the cookies to the class to count the chips? We will learn more about design in two weeks. 8. What is the difference between a population and a sample? Is the carton of cookies a population or a sample? 9. How do you think the cookies should be distributed? 10. What method of distribution did the class settle on? 11. Obtain a count for your cookie (please use the napkin to avoid a mess). How many chips are in your cookie? 12. Take a look at the data set collected by the class. How many variables are there? What name would you give the variable(s)? How many observations? Do you see any unusual features about the chip numbers recorded? Did anyone record fractions? Did anyone lose count and have already eaten half their cookie? Did anyone start without a cookie? Did anyone start with a broken cookie? Were any cookies not counted? Any other notes you think might be important for later data analysis? 2 3 Simpson’s Paradox Example - To Turn In A study in South Africa in 1990 attempted to study cardiovascular risk factors for children. Researchers attempted to enlist participants in the study from a compiled list of families with single births over the course of a seven week period in a metropolitan area. Researchers collected information from all participating families and then came back five years later, to do a follow-up. However, not all families chose to participate in the five year follow-up. Hence, researchers had to address possible differences between the first year sample and the smaller subset that was the five year sample. One of the variables collected for the first year sample was whether the participant mothers had medical aid (health care insurance for the mother, basically) at time of birth. The following table presents that data as well as whether the families participated in the five year study: Medical Aid No Medical Aid Total What What What What proportion proportion proportion proportion of of of of Participated 46 370 416 Did Not Part. 195 979 1174 Total 241 1349 1590 randomly selected families participated in the five year study? mothers had medical aid? mothers with medical aid participated in the study? mothers without medical aid participated in the study? Based on your calculations above, it should look like those with NO aid were more likely to participate! In studying risk factors, that could be a big issue. The researchers wanted to investigate further. Adding an additional variable, race of the mother, results in the following table: Medical Aid No Medical Aid Total White Participated Did 10 2 12 Not Part. 104 22 126 Black Participated Did 36 368 404 Not Part. 91 957 1048 Total 241 1349 1590 Compute the following proportions (to four decimal places): What proportion of white mothers with medical aid participated? What proportion of white mothers without medical aid participated? What proportion of black mothers with medical aid participated? What proportion of black mothers without medical aid participated? Within each race, which proportion was higher - the ones involving medical aid or no medical aid? Be sure you can explain what is going on (both tables) using your understanding of Simpson’s Paradox! 3