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# Chi-square test: Degree of certainity, Cockpit Noise & Cola

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1: 15.18 Sixty-eight 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 &#945; = .05, is the degree of certainty independent of credits earned? Certainty

Certainty of Major by Credits Earned

Credits Earned Very Uncertain Somewhat Certain Very Certain Row Total
0 - 9 12 8 3 23
10-59 8 6 10 24
60 or more 5 5 11 21
Col Total 25 19 24 68

2: 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 &#945; = .05, is the cockpit noise level independent of flight phase?

(Data are from Capt. Robert E. Hartl, retired.) Noise

Noise Readings by Flight Phase in B-727

Flight Phase
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

3: 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 &#945; = .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 &#960;1 = &#960;2 (see Chapter 10 - test of proportions) and test whether your results are the same as using the Chi-square test for independence. Which test is preferable? Why?

(Data are from Consumer Reports 56, no. 8 [August 1991], p. 519.) Cola

Note: You need to run or to calculate both a Chi-square test of independence and a test of two sample proportions. The sample size is 46, with 19 for the regular cola drinkers and 27 for the diet cola drinkers.

Can Cola Drinkers Tell The Difference?

Correct? Regular Cola Diet Cola Row Total
Yes 7 7 14
No 12 20 32
Col Total 19 27 46