Answered: A manufacturer claims that the mean…

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

A manufacturer claims that the mean lifetime, μ, of its light bulbs is 53months. The standard deviation of these lifetimes is

4 months. Twenty-six bulbs are selected at random, and their mean lifetime is found to be 52 months. Assume that the population is normally distributed. Can we conclude, at the 0.05 level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from 53 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? .
H0:?
H1:?
(b)	Determine the type of test statistic to use.
	▼(Choose one) z? T? chi sqauare ? or F?
(c)	Find the value of the test statistic.? (Round to three or more decimal places.)

(d)	Find the p-value. ? (Round to three or more decimal places.)
(e)	Can we conclude that the mean lifetime of light bulbs made by this manufacturer differs from 53 months? yes or no ?

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

Given

mu = 53

sigma = 4

n = 26

xbar = 52

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