Consider the propellant data is Exercise 11-13. Assume that strength less than 2100 psi is considered a failure. Relate propellant age to the probability of failure with a logistic regression model.

(a) Does age have a significant effect on the probability of failure at a = 0.05?

(b) What is the estimated probability of failure when the storage time is 18 weeks?

(c) What is the effect of a one-week increase in storage on the odds of failure?

(d) Construct a plot of the estimated probability of failure as a function of age.

Exercise 11-13

A rocket motor is manufactured by bonding together two types of propellants, an igniter and a sustainer. The shear strength of the bond y is thought to be a linear function of the age of the propellant x when the motor is cast. Table E11-4 provides 20 observations.

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Strength y (psi) Observation Age x (weeks) Number 2158.70 15.50 1678.15 23.75 3 2316.00 8.00 17.00 4 2061.30 2207.50 5.00 1708.30 19.00 24.00 1784.70 2.50 2575.00 2357.90 7.50 10 2277.70 11.00 11 2165.20 13.00 12 2399.55 3.75 13 1779.80 25.00 2336.75 14 9.75 1765.30 15 22.00 16 2053.50 18.00 6.00 17 2414.40 18 2200.50 12.50 2.00 19 2654.20 20 1753.70 21.50