For the 23 space shuttle flights before the Challenger mission disaster in 1986, Table 4.10 shows the temperature (◦F) at the time of the flight and whether at least one primary O-ring suffered thermal distress.

a. Use logistic regression to model the effect of temperature on the probability of thermal distress. Interpret the effect.

b. Estimate the probability of thermal distress at 31◦F, the temperature at the time of the Challenger flight.

c. At what temperature does the estimated probability equal 0.50? At that temperature, give a linear approximation for the change in the estimated probability per degree increase in temperature.

d. Interpret the effect of temperature on the odds of thermal distress.

e. Test the hypothesis that temperature has no effect, using (i) the Wald test,

(ii) the likelihood-ratio test.