Question

In: Statistics and Probability

A random sample of n = 15 heat pumps of a certain type yielded the following...

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

2.0     1.4     6.0     1.8 5.3 0.4     1.0     5.3
15.9 0.8 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

(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 using critical values that capture an area of 0.1 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-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.)

  ,

years

Solutions

Expert Solution


Related Solutions

A random sample of n = 15 heat pumps of a certain type yielded the following...
A random sample of n = 15 heat pumps of a certain type yielded the following observations on lifetime (in years): 2.0     1.4     6.0     1.9 5.2 0.4     1.0     5.3 15.6 0.9 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.)   , years (b) How should the interval of part...
A random sample of n = 15 heat pumps of a certain type yielded the following...
A random sample of n = 15 heat pumps of a certain type yielded the following observations on lifetime (in years): 2.0     1.4     6.0     1.6 5.1 0.4     1.0     5.3 15.7 0.7 4.8 0.9     12.3     5.3 0.6 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 What is a 95% CI...
A random sample of n = 15 heat pumps of a certain type yielded the following...
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 1.9 5.1 0.4 1.0 5.3 15.6 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 96% CI for expected (true average) lifetime (round answer to two decimal places) (________, _________) years c.) What is a 95% CI for...
A simple random sample of 16 adults drawn from a certain population of adults yielded a...
A simple random sample of 16 adults drawn from a certain population of adults yielded a mean weight of 63kg. Assume that weights in the population are approximately normally distributed with a variance of 49. Do the sample data provide sufficient evidence for us to conclude that the mean weight for the population is less than 70 kg? Let the probability of committing a type I error be .01. 1. Write the hypotheses, indicate the claim 2. find the critical...
A random sample of size n=500 yielded p̂ =0.08 a) Construct a 95% confidence interval for...
A random sample of size n=500 yielded p̂ =0.08 a) Construct a 95% confidence interval for p. b) Interpret the 95% confidence interval. c) Explain what is meant by the phrase "95% confidence interval."
A simple random sample of 12 e-readers of a certain type had the following minutes of...
A simple random sample of 12 e-readers of a certain type had the following minutes of battery life. 287, 311, 262, 392, 313, 304, 346, 316, 286, 274, 278, 291 Assume that it is reasonable to believe that the population is approximately normal and the population standard deviation is 63. What is the upper bound of the 95% confidence interval for the battery life for all e-readers of this type? Round your answer to one decimal places (for example: 319.4)....
A simple random sample of 12 e-readers of a certain type had the following minutes of...
A simple random sample of 12 e-readers of a certain type had the following minutes of battery life. 287, 311, 262, 392, 313, 260, 320, 316, 286, 256, 303, 291 Assume that it is reasonable to believe that the population is approximately normal and the population standard deviation is 76. What is the upper bound of the 95% confidence interval for the battery life for all e-readers of this type? Round your answer to one decimal places (for example: 319.4)....
A rivet is to be inserted into a hole. A random sample of n equals 15...
A rivet is to be inserted into a hole. A random sample of n equals 15 parts is selected and the hole diameter is measured. The sample standard deviation is millimeters. Is there strong evidence to indicate that the standard deviation of hole diameter exceeds 0.01 millimeters? Use (a) Calculate the test statistic Round your answer to two decimal places (e.g. 98.76). (b) Is there strong evidence to indicate that the standard deviation of hole diameter exceeds 0.01 millimeters?
A rivet is to be inserted into a hole. A random sample n=15 of parts is...
A rivet is to be inserted into a hole. A random sample n=15 of parts is selected, and the hole diameter is measured. The sample standard deviation of the hole diameter measurements is s=0.008 millimeters. Construct a 99% lower confidence bound for σ2 using MATLAB step by step . Please screenshot the MATLAB screen
n a random sample of 38 criminals convicted of a certain​ crime, it was determined that...
n a random sample of 38 criminals convicted of a certain​ crime, it was determined that the mean length of sentencing was 70 ​months, with a standard deviation of 5 months. Construct and interpret a 95​% confidence interval for the mean length of sentencing for this crime.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT