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# Chi square test

Directions: You may include the statistical software output, but you must also include a well-written explanation of the findings. Be sure to answer the question asked in each problem, and explain why, with reference to your output. If you calculate the answers manually, be sure to show your work. I would prefer a Word document with your answers below each problem, but you may also submit an Excel document. (Excel data sets are available in Course Materials forum as attachment.)

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

2. The safety director of Honda USA took samples at random from the file of minor accidents and classified them according to the time the accident took place. Using the goodness-of-fit test and the .01 level of significance, determine whether the accidents are evenly distributed (uniform) throughout the day. Write a brief explanation of your conclusion.

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

Chi-square Contingency Table Test for Independence

Col 1 Col 2 Col 3 Total
Row 1 Observed 6 2 6 14
Expected 5.74 1.84 6.43 14.00
O - E 0.26 0.16 -0.43 0.00
% of chisq 0.1% 0.1% 0.2% 0.4%
Row 2 Observed 18 3 8 29
Expected 11.89 3.80 13.31 29.00
O - E 6.11 -0.80 -5.31 0.00
% of chisq 20.8% 1.1% 14.0% 35.9%
Row 3 Observed 1 3 14 18
Expected 7.38 2.36 8.26 18.00
O - E -6.38 0.64 5.74 0.00
% of chisq 36.4% 1.1% 26.3% 63.8%
Total Observed 25 8 28 61
Expected 25.00 8.00 28.00 61.00
O - E 0.00 0.00 0.00 0.00
% of chisq 57.2% 2.4% 40.4% 100.0%

15.16 chi-square
4 df
.0044 p-value

.499 Phi coefficient
.446 Coefficient of Contingency
.353 Cramér's V

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 (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

#### Solution Summary

Step by step method for computing test statistic for hi square test is given in the answer.

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