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 below.

Part 9. What is the critical value? a) 1.72 b) -1.72 c) -3.63 d) 3.63

Part 10. What is the p-value? a) 0.00154 b) 0.00078 c) 0.05 d) 0.025

Part 11. 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

Part 12. 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

Answer 1

Result:

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 below.

Part 9. What is the critical value? a) 1.72 b) -1.72 c) -3.63 d) 3.63

Answer: b) -1.72

Part 10. What is the p-value? a) 0.00154 b) 0.00078 c) 0.05 d) 0.025

Answer b) 0.00078

Part 11. What is the rejection criteria?

Reject H0 if a) p-value < 0.05

Part 12. What is your conclusion?

a) Reject H0

Calculations:

Correlation Matrix
		Temperature	Damage
	Temperature	1.0000	-0.6215
	Damage	-0.6215	1.0000

Test for Correlation

H0: ρ = 0   

H1: ρ <  0    ( lower tail test)

t = -3.6355

DF = n-2 =21

Table value of t with 21 DF at 0.05 level = -1.72

Calculated t = -3.6355 < -1.72 , the table value

The null hypothesis is rejected.