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    Instructions In all exercises, include MegaStat, Excel, or MINITAB exhibits to support your calculations. State the hypotheses, show how the degrees of freedom are calculated, find the critical value of chi-square from Appendix E or from Excel's function =CHIINV(alpha, deg_freedom), and interpret the p-value. Tell whether the conclusion is sensitive to the level of significance chosen, identify cells that contribute the most to the chi-square test statistic, and check for small expected frequencies. If necessary, you can calculate the p-value by using Excel's function =CHIDIST(test statistic, deg_freedom). Note: Exercises marked * are harder or require optional material.

    15.18- Sixty-four students in an introductory college economics class were asked how many credits they had earned in college, and how certain they were about their choice of major. Research question: At α = .01, is the degree of certainty independent of credits earned? Certainty

    Credits Earned Very Uncertain Somewhat Certain Very Certain Row Total
    0-9 12 8 3 23
    10-59 8 4 10 22
    60 or more 1 7 11 19
    Col Total 21 19 24 64

    15.22- 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 by mall location? (Data are from a project by MBA students Steve Bennett, Alicia Morais, Steve Olson, and Greg Corda.) Vehicles

    Vehicle Type Somerset Oakland Great Lakes Jamestown Row Total
    Car 44 49 36 64 193
    Minivan 21 15 18 13 67
    Full-Sized Van 2 3 3 2 10
    SUV 19 27 26 12 84
    Truck 14 6 17 9 46
    Col Total 100 100 100 100 400

    15.24- High levels of cockpit noise in an aircraft can damage the hearing of pilots who are exposed to this hazard for many hours. A Boeing 727 co-pilot collected 61 noise observations using a handheld sound meter. Noise level is defined as "Low" (under 88 decibels), "Medium" (88 to 91 decibels), or "High" (92 decibels or more). There are three flight phases (Climb, Cruise, Descent). Research question: At α = .05, is the cockpit noise level independent of flight phase? (Data are from Capt. Robert E. Hartl, retired.) Noise

    Noise Level Climb Cruise Descent Row Total
    Low 6 2 6 14
    Medium 18 3 8 29
    High 1 3 14 18
    Col Total 25 8 28 61

    15.28- 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) 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

    Correct? Regular Cola Diet Cola Row Total
    Yes, got it right 7 7 14
    No, got it wrong 12 20 32
    Col Total 19 27 46

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