Question

Back in 1986 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 13. 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

Part 14. What is the upper bound? a) 10.14 b) 25.93 c) -0.35 d) -0.12

Part 15. 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

Part 16. 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

Part 17. 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

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

Part 13. 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

Part 14. What is the upper bound? a) 10.14 b) 25.93 c) -0.35 d) -0.12

Part 15. 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

Part 16. 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

Part 17. 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

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Using Excel<data<data analysis<regression

Regression Analysis
	r²	0.386
	r	-0.621
	Std. Error	2.147
	n	23
	k	1
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	90% lower	90% upper
Intercept	18.0356	4.59	3.93	0.00	10.14	25.93
	-0.2400	0.0660	-3.635	.0015	-0.3536	-0.1264

	99% Confidence Interval	99% Prediction Interval
Predicted	lower	upper	lower	upper
10.356	3.293	17.419	1.038	19.674