Discussion:
Q1: In a three-digit lottery, each of the three digits is supposed to have the same probability of occurrence (counting initial blanks as zeros, e.g., 32 is treated as 032). The table shows the frequency of occurrence of each digit for 90 consecutive daily three-digit drawings. (a) Make a bar chart and describe it. (b) Calculate expected frequencies for each class. (c) Perform the chi-square test for a uniform distribution. At α = .05, can you reject the hypothesis that the digits are from a uniform population?
Lottery3
Digit Frequency
0 33
17
2 25
3 30
31
5 28
6 24
7 25
8 32
9 25
Total 270
Q2: A student team examined parked cars in four different suburban shopping malls. One hundred vehicles were examined in each location. Research question: At α = .05, does vehicle type vary bymall location? (Data are from a project by MBA students Steve Bennett, Alicia Morais, Steve Olson, and Greg Corda.)
Vehicles Somerset oakland great lakes jamestown row total
Vehicle Toe 44 49 36 64 193
Car 21 15 18 13 67
Minivan 2 3 3 2 10
Full dized Van SW 19 27 26 12 84
Truck 14 6 17 9 46
Col Total 100 100 100 100 400
Q3: Can people really identify their favorite brand of cola? Volunteers tasted Coca-Cola Classic, Pepsi, Diet Coke, and Diet Pepsi, with the results shown below. Research question: At α = .05, is the correctness of the prediction different for the two types of cola drinkers? Could you identify your favorite brand in this kind of test? Since it is a 2 × 2 table, try also a two-tailed two-sample z test for π1 = π2 (see Chapter 10) and verify that z2 is the same as your chi-square statistic.Which test do you prefer? Why? (Data are from Consumer Reports 56, no. 8 [August 1991], p. 519.)
Cola
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Correct?
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Regular Cota Diet Cola
|
Raw Total
|
|
Yes, got it right
|
7
|
7
|
14
|
|
No, got it wrong
|
12
|
20
|
32
|
|
Col Total
|
19 27
|
46
|