A random sample of n = 15 heat pumps of a certain type yielded the following observations on lifetime (in years):2.06.0 1.6 5.4 0.4 1.0 5.31.215.8 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.)0.030.98years(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.)2.697.53years

(a) The mean of the exponential distribution is given by, E[X] = 1/λ The 95% confidence interval…

Answered: A random sample of n = 15 heat pumps of…

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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Cardiologists use the short-range scaling exponent α1, which measures the randomness of heart rate patterns, as a tool to assess risk of heart attack. The article “Applying Fractal Analysis to Short Sets of Heart Rate Variability Data” compared values of α1 computed from long series of measurements (approximately 40,000 heartbeats) with those estimated from the first 300 beats to determine how well the long-term measurement (y) could be predicted the short-term one (x). Following are the data (obtained by digitizing a graph). Short Long 0.54 0.55 1.02 0.79 1.4 0.81 0.88 0.9 1.68 1.05 1.16 1.05 0.82 1.05 0.93 1.07 1.26 1.1 1.18 1.19 0.81 1.19 0.81 1.2 1.28 1.23 1.18 1.23 0.71 1.24 Note: This problem has a reduced data set for ease of performing the calculations required. This differs from the data set given for this problem in the text. Find a 95% confidence interval for the mean long-term measurement for those with short-term measurements…
Cardiologists use the short-range scaling exponent α1, which measures the randomness of heart rate patterns, as a tool to assess risk of heart attack. The article “Applying Fractal Analysis to Short Sets of Heart Rate Variability Data” compared values of α1 computed from long series of measurements (approximately 40,000 heartbeats) with those estimated from the first 300 beats to determine how well the long-term measurement (y) could be predicted the short-term one (x). Following are the data (obtained by digitizing a graph). Short Long 0.54 0.55 1.02 0.79 1.4 0.81 0.88 0.9 1.68 1.05 1.16 1.05 0.82 1.05 0.93 1.07 1.26 1.1 1.18 1.19 0.81 1.19 0.81 1.2 1.28 1.23 1.18 1.23 0.71 1.24 Note: This problem has a reduced data set for ease of performing the calculations required. This differs from the data set given for this problem in the text. A. Compute the least-squares line for predicting the long-term measurement from the short-term measurement.…
Sales delay is the elapsed time between the manufacture of a product and its sale. According an article it is quite common for investigators to model sales delay using a lognormal distribution. For a particular product, the cited article proposes this distribution with parameter values = 2.02 and ² = 0.04 (here the unit for delay is months). USE SALT (a) What are the variance and standard deviation of delay time? (Round your answers to two decimal places.) variance 3.39 X months² months standard deviation (b) What is the probability that delay time exceeds 12 months? (Round your answer to four decimal places.) (c) What is the probability that delay time is within one standard deviation of its mean value? (Round your answer to four decimal places.) (d) What is the median of the delay time distribution? (Round your answer to two decimal places.) months (e) What is the 99th percentile of the delay time distribution? (Round your answer to two decimal places.) months (f) Among 10 randomly…
Q1: Lifetimes of a certain component are lognormally distributed with parameters u = 1 day and o = 0.5 days. Find the mean lifetime of these components. 1-Find the standard deviation of the lifetimes. 2-Find CDF 3- Find reliability at t= 4 day
Suppos are interested in studying a population to estimate its mean. The population is normal and has a standard deviation of G=23. We have taken a random sample of size 11=95 from the population. This is Sample 1 in the table below. (In the table, Sample 1 is written "S1", Sample 2 is written "S2", etc.) As shown in the table, the sample mean of Sample 1 is = 142.0. Also shown are the lower and upper limits of the 80% confidence interval for the population mean using this sample, as well as the lower and upper limits of the 95% confidence interval. Suppose that the true mean of the population is = 140, which is shown on the displays for the confidence intervals. Press the "Generate Samples" button to simulate taking 19 more random samples of size 11 = 95 from this same population. (The 80% and 95% confidence intervals for all of the samples are shown in the table and graphed.) Then complete parts (a) through (c) below the table. 80% 80% 95% 95% lower upper lower upper limit limit…
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