For the 23 space shuttle flights before the challenger mission disaster in 1986, Table 5.12 shows the temperature 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. Plot a figure of the fitted model, and interpret.

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

c. Construct a confidence interval for the effect of temperature on the odds of thermal distress, and test the statistical significance of the effect.

Table 5.12:

TD Ft Temp TD|Ft Temp TD|Ft Temp TD Ft Temp TD Ft Temp 2 70 73 1 66 69 67 5 10 63 15 67 20 79 68 57 6. 72 70 13 67 18 81 58 12 14 53 11 70 78 75 70 19 16 17 76 0 23 21 75 22 1 76