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# Chi square: Is the cockpit noise level independent of flight

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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 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

1. State the hypotheses.

2. Show how the degrees of freedom are calculated.
3. Find the critical value of chi square from Appendix E or from Excel's function =CHIINV(alpha, deg_freedom).
4. Compute the value of the chi square test statistic.
5. Compute and interpret the p-value. If necessary, you can calculate the p-value by using Excel's function =CHIDIST(test statistic,deg_freedom).

7. Tell whether this conclusion is sensitive to the level of significance chosen.
8. Identify cells that contribute the most to the chi-square test statistic.
9. Check for small expected frequencies.