Question

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 at “HW08_Q1.xls”.

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) + Є b) O-RING = 18.03 -0.23(TEMP) c) O-RING = 18.03 -0.23(TEMP) + Є d) O-RING = 18.03 +0.23(TEMP) + Є

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: β1 = 0, Ha: β1 > 0 b) H0: β1 = 0, Ha: β1 < 0 c) H0: β1 = 0, Ha: β1 ≠ 0 d) H0: β0 = 0, Ha: β0 < 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 p-value? a) 0.00154 b) 0.00078 c) 0.05 d) 0.025

Q10. 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

Q11. What is your conclusion? a) Reject H0 b) Fail to Reject H0 c) Reject Ha d) Fail to Reject Ha

Q12. 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

Q13. What would be the correlation between the O-ring damage index and the temperature? a) 0.62 b) -0.62 c) 0.38 d) -0.38

Flight number Temperature O-ring damage index
1 66 0
2 70 4
3 69 0
5 68 0
6 67 0
7 72 0
8 73 0
9 70 0
10 57 4
11 63 2
12 70 4
13 78 0
14 67 0
15 75 0
16 53 11
17 67 0
18 81 0
19 70 0
20 67 0
21 79 0
22 75 4
23 76 0
24 58 4

Answer 1

1)b)Dependent - O ring damage

Independent - Temperature

2)b)Yes,From the scatter plot , we get a decreasing pattern and with the help of correlation coefficient(-0.621) to find the association.

3)c)The least square regression equation is given as

O-RING = 18.03 -0.23(TEMP)

4)a)The meaning of in the problem is Expected value of the o-ring damage when the temperature is zero

5)c) The meaning of is  Expected decrease in the o-ring damage when the temperature goes up by one unit

6)c) The hypothesis for the claim is

7) To test the hypothesis, we can use a)t-test.

8)The value of test statistic is c)-3.63

9)The p value is d)0.025

10) Rejection criteria is reject if a)p-value < 0.05

11)The conclusion is a) Reject since p-value(0.025) < 0.05

12)The O-ring damage for an atmospheric pressure of 32F is 18.03 -0.23(32) = a)25.3

13)The correlation coefficient between O-ring damage index and the temperature is b)-0.62