A random sample of n = 15 heat pumps of a certain type yielded the following observations on lifetime (in years): 5.4 0.4 1.0 5.3 2.0 1.2 15.8 0.7 6.0 1.6 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.) years 1.7233 X 6.6967 x (b) How should the interval of part (a) be altered to achieve a confidence level of 99%? O 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. O 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. confidence level requires using critical values that capture an area of 0.005 in each tail of the chi-squared distribution. ⒸA 99% O A 99% confidence level requires using critical values that 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.) 3.4520 x 6.0192 x) years You may need to use the appropriate table in the Appendix of Tables to answer this question.
A random sample of n = 15 heat pumps of a certain type yielded the following observations on lifetime (in years): 5.4 0.4 1.0 5.3 2.0 1.2 15.8 0.7 6.0 1.6 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.) years 1.7233 X 6.6967 x (b) How should the interval of part (a) be altered to achieve a confidence level of 99%? O 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. O 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. confidence level requires using critical values that capture an area of 0.005 in each tail of the chi-squared distribution. ⒸA 99% O A 99% confidence level requires using critical values that 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.) 3.4520 x 6.0192 x) years You may need to use the appropriate table in the Appendix of Tables to answer this question.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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GLA2.3
![A random sample of n = 15 heat pumps of a certain type yielded the following observations on lifetime (in years):
1.2 6.0 1.6
5.4 0.4 1.0 5.3
2.0
15.8 0.7 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.)
x
1.7233
x
6.6967
years
(b) How should the interval of part (a) be altered to achieve a confidence level of 99%?
O 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.
O 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 critical values that capture an area of 0.005 in each tail of the chi-squared distribution.
O A 99% confidence level requires using critical values that 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.)
3.4520
x years
x
6.0192
You may need to use the appropriate table in the Appendix of Tables to answer this question.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff88cb2ec-9620-4132-9b3d-55b25de3b1b6%2Ff53898fd-edf0-4217-9b95-0a26cd2f914c%2Fz47wzc8_processed.png&w=3840&q=75)
Transcribed Image Text:A random sample of n = 15 heat pumps of a certain type yielded the following observations on lifetime (in years):
1.2 6.0 1.6
5.4 0.4 1.0 5.3
2.0
15.8 0.7 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.)
x
1.7233
x
6.6967
years
(b) How should the interval of part (a) be altered to achieve a confidence level of 99%?
O 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.
O 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 critical values that capture an area of 0.005 in each tail of the chi-squared distribution.
O A 99% confidence level requires using critical values that 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.)
3.4520
x years
x
6.0192
You may need to use the appropriate table in the Appendix of Tables to answer this question.
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