Question

A random sample of n = 15 heat pumps of a certain type yielded the following observations on lifetime (in years):
2.0 1.1 6.0 1.7 5.3 0.4 1.0 5.3
15.7 0.9 4.8 0.9 12.2 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 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 usingcritical 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 of0.1 in each tail of the chi-squared distribution. A 99% confidence level requires using critical values that capture an area of 0.005 in each tail of the chi-squareddistribution.

(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 youranswers to two decimal places.)

Answer 1

First we have to calculate the sample mean and sample standarddeviation
VariableMeanStDev
life time 4.21(x-bar)4.49 (s)

The formulae for calculating the95% CI for expected (true average)lifetime is givenby

HEre t_α/2= 2.145
Substitute the values we have

solve the above we get the answer