The lightbulbs in an industrial warehouse have been found to have a mean lifetime of 1030.0 hours. The warehouse manager has been approached by a representative of Extendabulb, a company that makes a device intended to increase bulb life. The manager is concerned that the average lifetime of Extendabulb-equipped bulbs might not be any greater than the 1030 hours historically experienced. In a subsequent test, the manager tests 22 bulbs equipped with the device and finds their mean life to be 976.82 hours. The underlying data are in lifetime.csv datafile. lifetime 878 1108 1141 935 930 884 912 1174 655 589 1077 875 1079 787 974 990 829 1140 1077 1220 997 1239 Use R or otherwise to indicate which one of the following best answers the manager’s question. a. The p.value of the test is 0.9197. We can conclude that there is no evidence to reject the null hypothesis of the mean lifetime of all lightbulbs produced in the warehouse is 1030.0 hours at significance level of 0.05. b. The p.value of the test is 0.0803. We can conclude that there is no evidence to reject the null hypothesis of the mean lifetime of all lightbulbs produced in the warehouse is 1030.0 hours at significance level of 0.05. c. The p.value of the test is 0.160

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 lightbulbs in an industrial warehouse have been found to have a mean lifetime of 1030.0 hours. The warehouse manager has been approached by a representative of Extendabulb, a company that makes a device intended to increase bulb life. The manager is concerned that the average lifetime of Extendabulb-equipped bulbs might not be any greater than the 1030 hours historically experienced. In a subsequent test, the manager tests 22 bulbs equipped with the device and finds their mean life to be 976.82 hours. The underlying data are in lifetime.csv datafile.

lifetime
878
1108
1141
935
930
884
912
1174
655
589
1077
875
1079
787
974
990
829
1140
1077
1220
997
1239

Use R or otherwise to indicate which one of the following best answers the manager’s question.
a. The p.value of the test is 0.9197. We can conclude that there is no evidence to reject the null hypothesis of the mean lifetime of all lightbulbs produced in the warehouse is 1030.0 hours at significance level of 0.05.

b. The p.value of the test is 0.0803. We can conclude that there is no evidence to reject the null hypothesis of the mean lifetime of all lightbulbs produced in the warehouse is 1030.0 hours at significance level of 0.05.

c. The p.value of the test is 0.1605. We can conclude that there is evidence to reject the null hypothesis of the mean lifetime of all lightbulbs produced in the warehouse is 1030.0 hours at significance level of 0.05.

d. The p.value of the test is 0.1605. We can conclude that there is no evidence to reject the null hypothesis of the mean lifetime of all lightbulbs produced in the warehouse is 1030.0 hours at significance level of 0.05.

e. The p.value of the test is 0.0803. We can conclude that there is evidence to reject the null hypothesis of the mean lifetime of all lightbulbs produced in the warehouse is 1030.0 hours at significance level of 0.05.

f. The p.value of the test is 0.9197. We can conclude that there is evidence to reject the null hypothesis of the mean lifetime of all lightbulbs produced in the warehouse is 1030.0 hours at significance level of 0.05.

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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