ADMN 950 - Homework No: 06 On January 28, 1986, the space shuttle Challenger exploded, and seven astronauts were killed. Prior to the launch, when predicted atmospheric temperature was for freezing weather at the launch site, engineers for Morton Thiokol (the manufacturer of the rocket motor) prepared charts to make the case that the launch should not take place due to the cold weather. These arguments were rejected, and the launch tragically took place. Upon investigation after the tragedy, experts agreed that the disaster occurred because of leaky rubber O-rings that did not seal properly due to the cold temperature. Data indicating the atmospheric temperature at the time of 23 previous launches and the O-ring damage index are given in the file "Shuttle.csv". Q1. Identify your independent and dependent variables. a) Independent: O-ring damage, Dependent: Temperature b) Independent: Temperature, Dependent: O-ring damage c) Independent: Time of the launch, Dependent: Temperature d) Independent: O-ring damage, Dependent: Time of the launch Q2. Plot a scatter diagram. Do you think it is reasonable to use the least squares regression method? a) No b) Yes c) Impossible to obtain a scatter plot d) There is not enough information to answer the question Q3. Use the least squares method to find the regression equation. Report your regression equation. a) TEMP= 18.03 -0.23(O-RING) + b) O-RING = 18.03 -0.23(TEMP) c) O-RING = 18.03 -0.23(TEMP) + d) O-RING = 18.03 +0.23(TEMP) + Q4. Interpret the meaning of 0 in the context of the problem. a) Expected value of the o-ring damage when the temperature is zero b) Expected value of the temperature when the o-ring damage is zero c) Expected decrease in the o-ring damage when the temperature is zero d) Expected decrease in the temperature when the o-ring damage is zero Q5. Interpret the meanings of 1 in the context of the problem. a) Expected decrease in the o-ring damage when the temperature goes down by one unit b) Expected value of the temperature when the o-ring damage is zero c) Expected decrease in the o-ring damage when the temperature goes up by one unit d) Expected decrease in the temperature when the o-ring damage goes up by one unit

Do you think that the engineers' claim at Morton Thiokol was reasonable (use an alpha of 0.05)? Q6. Please state your hypothesis. a) H0: 1 = 0, Ha: 1 > 0 b) H0: 1 = 0, Ha: 1 < 0 c) H0: 1 = 0, Ha: 1 0 d) H0: 0 = 0, Ha: 0 < 0 Q7. What type of test you will be using to test the hypothesis? a) t-test b) independent samples t-test c) F-test d) z-test Q8. What is the value of the test statistic? a) 3.63 b) 3.93 c) -3.63 d) -3.93 Q9. What is the critical value? a) 1.72 b) -1.72 c) -3.63 d) 3.63 Q10. What is the p-value? a) 0.00154 b) 0.00078 c) 0.05 d) 0.025 Q11. What is the rejection criteria? Reject H0 if a) p-value < 0.05 b) p-value < 0.10 c) p-value < 0.025 d) p-value > 0.05 Q12. What is your conclusion? a) Reject H0 b) Fail to Reject H0 c) Reject Ha d) Fail to Reject Ha Q13. Obtain a 90% confidence interval for the slope coefficient. What is the lower bound? a) 10.14 b) 25.93 c) -0.35 d) -0.12 Q14. What is the upper bound? a) 10.14 b) 25.93 c) -0.35 d) -0.12 Q15. Based on your regression equation, what would your prediction of the O-ring damage for an atmospheric temperature of 32F, the temperature on the morning of the launch of Challenger. a) 25.3 b) 10.6 c) 32 d) 8.1 Q16. What is the upper bound for a 99% prediction interval for your prediction from question 15? a) 19.67 b) 25.3 c) 32 d) 99 Do you think that the engineers' claim at Morton Thiokol was reasonable (use an alpha of 0.05)? Q6. Please state your hypothesis. a) H0: 1 = 0, Ha: 1 > 0 b) H0: 1 = 0, Ha: 1 < 0 c) H0: 1 = 0, Ha: 1 0 d) H0: 0 = 0, Ha: 0 < 0 Q7. What type of test you will be using to test the hypothesis? a) t-test b) independent samples t-test c) F-test d) z-test Q8. What is the value of the test statistic? a) 3.63 b) 3.93 c) -3.63 d) -3.93 Q9. What is the critical value? a) 1.72 b) -1.72 c) -3.63 d) 3.63 Q10. What is the p-value? a) 0.00154 b) 0.00078 c) 0.05 d) 0.025 Q11. What is the rejection criteria? Reject H0 if a) p-value < 0.05 b) p-value < 0.10 c) p-value < 0.025 d) p-value > 0.05 Q12. What is your conclusion? a) Reject H0 b) Fail to Reject H0 c) Reject Ha d) Fail to Reject Ha Q13. Obtain a 90% confidence interval for the slope coefficient. What is the lower bound? a) 10.14 b) 25.93 c) -0.35 d) -0.12 Q14. What is the upper bound? a) 10.14 b) 25.93 c) -0.35 d) -0.12 Q15. Based on your regression equation, what would your prediction of the O-ring damage for an atmospheric temperature of 32F, the temperature on the morning of the launch of Challenger. a) 25.3 b) 10.6 c) 32 d) 8.1 Q16. What is the upper bound for a 99% prediction interval for your prediction from question 15? a) 19.67 b) 25.3 c) 32 d) 99

Q17. What is the correlation between the O-ring damage index and the temperature? a) 0.62 b) -0.62 c) 0.38 d) -0.38 Q17. What is the correlation between the O-ring damage index and the temperature?