Answered: According to a report done by S & J…

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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According to a report done by S & J Power, the mean lifetime of the light bulbs it manufactures is 52 months. A researcher for a consumer advocate group tests this by selecting 150 bulbs at random. For the bulbs in the sample, the mean lifetime is 51 months. It is known that the population standard deviation of the lifetimes is 7 months. Can we conclude, at the 0.01 level of significance, that the population mean lifetime, μ, of light bulbs made by this manufacturer differs from 52 months? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below.

a. State the null hypothesis H0 and the alternative hypothesis H1.

b. Find the value of the test statistic. Round to three or more decimals.

c. Find the p-value. Round to three or more decimals.

d. Can we conclude that the population mean lifetime of light bulbs made by this manufacturer differs from 52 months?

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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