Question

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

2.0	1.2	6.0	1.8	5.1	0.4	1.0	5.3
15.7	0.8	4.8	0.9	12.4	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.)

(b) How should the interval of part (a) be altered to achieve a confidence level of 99%?

A 99% confidence level requires using critical values that capture an area of 0.005 in each tail of the chi-squared distribution.A 99% confidence level requires using critical values that capture an area of 0.1 in each tail of the chi-squared distribution.    A 99% confidence level requires using a new value of n to capture an area of 0.005 in each tail of the chi-squared distribution.A 99% confidence level requires using a new value of n to capture an area of 0.1 in each tail of the chi-squared distribution.

(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.

Answer 1

a)

for 95 % confidence and 2*n=30 degree of freedom crtiical values from chi square distribution are 16.791 and 46.979
therefore 95 % confidence interval for mean=(2∑x/46.979,2∑x/16.791)=(2.69,7.54)

b)

A 99% confidence level requires using critical values that capture an area of 0.005 in each tail of the chi-squared distribution.

c)

for standard deviation is equal to mean in case of exponential distribution:

95 % confidence interval =(2∑x/46.979,2∑x/16.791)=(2.69,7.54)