11.1 Chi-Square Test for Goodness of Fit A local bank wants to evaluate the usage of its ATM. They assume that the machine is used consistently throughout the wee k, including weekends. The bank recorded the number of times their ATM was used over the course of a week: D_ay ii of Times Used Monday 38 Tuesday 33 Wednesday 41 Thursday 25 Friday 22 Saturday 38 Sunday 45 1. In words, how would you phrase your HD and Ha? 2. Mathematically, how would you phrase your HD and Ha? 3. Assuming the number of customers does not vary from day to day, what are your expected probabilities for each day? What are your expected raw values? 4. What is your df? 5. You calculate )F = 12.31 {feel free to figure this out on your own). At the .05 level, do you accept or reject H0? 11.2 Chi-Square Test for Goodness of Fit A nearby bar serves bone-in buffalo wings. In terms of flavors offered, they typically sell the following proportions: 20% Spicy Garlic, 50% Classic Medium, 10% Teriyaki, 10% Hot BBQ, and 10% Asian Zing. After running a campaign to promote their new boneless wings, they wonder if their customers have the same flavor preferences. After offering these new boneless wings for 10 days and tracking the number of each flavor sold, they examine the results below: Boneless Flavor if 50ch Spicy Garlic 251 Classic Medium 630 Teriyaki 115 Hot BBQ 141 Asian Zing 121 1. In words, how would you phrase your HD and Ha? 2. Mathematically, how would you phrase your HD and Ha? 3. Assuming that flavor preference does not vary between bone-in and boneless wings, what are your expected probabilities for each flavor? What are your expected raw values? 4. What is your df? 5. You calculate X2 = 2.95 {feel free to figure this out on your own). At the .05 level, do you accept or reject H0? 11.3 Chi-Squa re Test for Association Thinking that there might be a dependent relationship between gender and choice of car color, we took a random sample of 1000 cars parked in the various lots throughout the university campus. The results are summarized below: White Black M Other TOTAL Male 190 117 215 53 575 Female 115 142 113 55 425 TOTAL 305 259 328 108 1000 1. In words, how would you phrase your Ho and Ha? 2. What is your df? 3. You calculate X2 = 30.81 (feel free to figure this out on your own). At the .01 level, do you accept or reject H0? 11.4 Chi-Square Test for Association Doing a marketing study for a nearby soft drink company, you are interested in knowing whether there is a relationship between cola preference and age. A random sample of 800 people is chosen for a taste test. The results of the study are shown below: Cola A Cola B Cola C TOTAL 30 and under 94 102 105 301 31 - 59 99 97 86 282 60 and over 68 73 75 217 TOTAL 261 272 267 800 1. In words, how would you phrase your H0 and Ha? 2. What is your df? 3. You calculate X2 = 1.93 {feel free to figure this out on your own). At the .005 level, do you accept or reject Ho