Shared leadership in airplane crews. Refer to the Human Factors (Mar. 2014) study of shared leadership by the cockpit and cabin crews of a commercial airplane, Exercise 9.13 (p. 476). Recall that simulated flights were taken by 84 six-person crews, where each crew consisted of a two-person cockpit (captain and first officer) and a four-person cabin team (three flight attendants and a purser). During the simulation, smoke appeared in the cabin and the reactions of the crew were monitored for teamwork. One key variable in the study was team goal attainment score, measured on a 0-to-60-point scale. Multiple regression analysis was used to model team goal attainment (y) as a function of the independent variables job experience of purser

(x1), job experience of head flight attendant (x2), gender of purser (x3), gender of head flight attendant (x4), leadership score of purser (x5), and leadership score of head flight attendant (x6).

a. Write a complete, first-order model for E(y) as a function of the six independent variables.

b. Consider a test of whether the leadership score of either the purser or head flight attendant (or both) is statistically useful for predicting team goal attainment.

Give the null and alternative hypotheses as well as the reduced model for this test.

c. The two models were fit to the data for the n = 60 successful cabin crews with the following results:

R2

= .02 for reduced model, R2

= .25 for complete model. Based on this information only, give your opinion regarding the null hypothesis for successful cabin crews.

d. The p-value of the subset F-test for comparing the two models for successful cabin crews was reported in the article as p 6 .05. Formally test the null hypothesis using a = .05. What do you conclude?

e. The two models were also fit to the data for the n = 24 unsuccessful cabin crews with the following results: R2

= .14 for reduced model, R2

= .15 for complete model. Based on this information only, give your opinion regarding the null hypothesis for unsuccessful cabin crews.

f. The p-value of the subset F-test for comparing the two models for unsuccessful cabin crews was reported in the article as p 7 .10. Formally test the null hypothesis using a = .05. What do you conclude?