Answered: The researcher tries to understand the…

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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Question

The researcher tries to understand the duration of guarantee time that a computer company is logical or not. Past records show time duration of guarantee has a normal distribution with mean 2 years and standard deviation of hundred days. A random sample of 16 computers that need repairmen is examined and mean time of usage is found as two and a half years and standard deviation of 4 months. Assuming that a year is 360 days and a month is 30 days for simplicity. Construct 695 confidence interval for mean life time usage for guarantee for the computer. (use two decimals)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution

Step 1

$G i v e n, s a m p l e s i z e (n) = 16 s a m p l e m e a n (x) = 2.5 y e a r s = 30 m o n t h s S \tan d a r d d e v i a t i o n (S) = 4 m o n t h s d e g r e e s o f f r e e d o m (d f) = n - 1 = 16 - 1 = 15 α = 1 - 0.95 = 0.05 \frac{α}{2} = 0.025 t_{0.025} (15) = 2.131 (f r o m t - t a b l e)$