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Name: The quality-control manager at a compact fluorescent light bulb (CFL
Uploaded: 2024-03-20T07:07:12.000Z
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Description: The quality-control manager at a compact fluorescent light bulb (CFL) factory needs to determine whether the mean life of a large shipment of CFLs is equal to 7,537 hours. The population standard deviation is 700 hours. A random sample of 49 light

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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The quality-control manager at a compact fluorescent light bulb (CFL) factory needs to determine whether the mean life of a large shipment of CFLs is equal to 7,537 hours. The population standard deviation is 700 hours. A random sample of 49 light bulbs indicates a sample mean life of

7,387 hours.

a. At the 0.05 level of significance, is there evidence that the mean life is different from 7,537 hours

What is/are the critical value(s)?

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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Step 1

Given Information:

Mean life of a large shipment of CFLs is equal to 7,537 hours. i.e., $μ_{0} = 7, 537$

Population standard deviation $σ = 700$

Sample size $n = 49$

Sample mean $\bar{x} = 7, 387$

Significance level $α = 0.05$

State the hypothesis as follows:

Null Hypothesis : $H_{0} : μ = 7, 537$ i.e., the mean life of a large shipment of CFLs is equal to 7,537 hours.

Alternative Hypothesis : $H_{1} : μ \neq 7, 537$ i.e., the mean life of a large shipment of CFLs is different from 7,537 hours.

This is a two tailed test.

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