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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 week, including weekends. The bank recorded the number of times their

ATM was used over the course of a week:

Day # 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 H0 and Ha?

2. Mathematically, how would you phrase your H0 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 X2 = 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 # Sold

Spicy Garlic 251

Classic Medium 630

Teriyaki 115

Hot BBQ 141

Asian Zing 121

1. In words, how would you phrase your H0 and Ha?

2. Mathematically, how would you phrase your H0 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-Square 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 Red 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 H0 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 76 217

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 H0?