Question

In: Statistics and Probability

Data indicating the atmospheric temperature at the time of 23 previous launches and the O-ring damage...

Data indicating the atmospheric temperature at the time of 23 previous launches and the O-ring damage index are given below.

The year was 1986 and 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 below.

Part 5. 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)?
Part 6. 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

Part 7. 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

Part 8. What is the value of the test statistic? a) 3.63 b) 3.93 c) -3.63 d) -3.93

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

Flight number

Temperature

Damage

1

66

0

2

70

4

3

69

0

5

68

0

6

67

0

7

72

0

8

73

0

9

70

0

41-B

57

4

41-C

63

2

41-D

70

4

41-G

78

0

51-A

67

0

51-B

75

0

51-C

53

11

51-D

67

0

51-F

81

0

51-G

70

0

51-I

67

0

51-J

79

0

61-A

75

4

61-B

76

0

61-C

58

4

Solutions

Expert Solution

Part 5. Interpret the meanings of ?1 in the context of the problem.
c) Expected decrease in the o-ring damage when the temperature goes up by one unit

Do you think that the engineers’ claim at Morton Thiokol was reasonable (use an alpha of 0.05)?
Part 6. Please state your hypothesis. c) H0: β1 = 0, Ha: β1 ≠ 0

Part 7. What type of test you will be using to test the hypothesis? a) t-test

Part 8. What is the value of the test statistic? c) -3.63

Part D. What is your conclusion? a) Reject H0

0.386
r   -0.621
Std. Error   2.147
n   23
k   1
Dep. Var. Damage
ANOVA table
Source SS   df   MS F p-value
Regression 60.8941 1   60.8941 13.22 .0015
Residual 96.7581 21   4.6075
Total 157.6522 22  
Regression output confidence interval
variables coefficients std. error    t (df=21) p-value 95% lower 95% upper
Intercept 18.0356
Temperature -0.2400 0.0660 -3.635 .0015 -0.3773 -0.1027

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