Question

A random sample of n = 15 heat pumps of a certain type yielded the following observations on lifetime (in years):

2.0	1.5	6.0	1.7	5.3	0.4	1.0	5.3
15.8	0.5	4.8	0.9	12.1	5.3	0.6

(a) Assume that the lifetime distribution is exponential and use an argument parallel to that of this example to obtain a 95% CI for expected (true average) lifetime. (Round your answers to two decimal places.) ( , ) years

c) What is a 95% CI for the standard deviation of the lifetime distribution? [Hint: What is the standard deviation of an exponential random variable?] (Round your answers to two decimal places.) ( , ) years

Answer 1

solutions & Given n=15, 2= 4:21,5= 4.5103 df = n-1 = 15-1 = 14. At 95% confidence tap. = 2.145 The 95% confiducenternal for Mil- i I taveltam) - 4.21† 2.145 (951031 = 4.21€ 2.50 = (1.71, 6:71) 2.2 Here from X2 table df = 2-1 = 15-1= 14 122 = 5.629 Xindy = 26.119 The 95% confidence internal foro ci- LOS as 2 a * | - | 14( 4.5103)? Tru.s 103) sos son s.629 T1414.5103) 1 26.119 = PLEASE LIKE. So$ 7.113 = 3.302