In tests of a computer component, it is found that the mean time between failures is 917 hours. A modification is made which is supposed to increase reliability by increasing the time between failures. Tests on a sample of 25 modified components produce a mean time between failures of 963 hours. Using a 1% level of significance, perform a hypothesis test to determine whether the mean time between failures for the modified components is greater than 917 hours. Assume that the population standard deviation is 57 hours. H0 : =μ917 hours H1 : >μ917 hours Test statistic : =z4.04 Critical value : =z2.33 Reject the null hypothesis. There is sufficient evidence to support the claim that, for the modified components, the mean time between failures is greater than 917 hours. H0 : >μ963 hours H1 : =μ963 hours Test statistic : =z80.44 Critical value : =z1.65 Reject the null hypothesis. There is sufficient evidence to support the claim that, for the modified components, the mean time between failures is greater than 963 hours. H0 : =μ963 hours H1 : >μ963 hours Test statistic : =z4.04 Critical value : =z2.33 Reject the null hypothesis. There is sufficient evidence to support the claim that, for the modified components, the mean time between failures is greater than 963 hours. H0 : >μ963 hours H1 : =μ963 hours Test statistic : =z4.04 Critical value : =z1.65 Reject the null hypothesis. There is sufficient evidence to support the claim that, for the modified components, the mean time between failures is greater than 963 hours.

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

In tests of a computer component, it is found that the mean time between failures is

917

hours. A modification is made which is supposed to increase reliability by increasing the time between failures. Tests on a sample of

modified components produce a mean time between failures of

963

hours. Using a

level of significance, perform a hypothesis test to determine whether the mean time between failures for the modified components is greater than

917

hours. Assume that the population standard deviation is

hours.

=μ917

hours

>μ917

hours
Test statistic :

=z4.04

Critical value :

=z2.33

Reject the null hypothesis. There is sufficient evidence to support the claim that, for the modified components, the mean time between failures is greater than

917

hours.

>μ963

hours

=μ963

hours
Test statistic :

=z80.44

Critical value :

=z1.65

Reject the null hypothesis. There is sufficient evidence to support the claim that, for the modified components, the mean time between failures is greater than

963

hours.

=μ963

hours

>μ963

hours
Test statistic :

=z4.04

Critical value :

=z2.33

Reject the null hypothesis. There is sufficient evidence to support the claim that, for the modified components, the mean time between failures is greater than

963

hours.

>μ963

hours

=μ963

hours
Test statistic :

=z4.04

Critical value :

=z1.65

Reject the null hypothesis. There is sufficient evidence to support the claim that, for the modified components, the mean time between failures is greater than

963

hours.

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 + ...

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