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Name: BIG Corporation advertises that its light bulbs have a mean lifetime,
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Description: BIG Corporation advertises that its light bulbs have a mean lifetime, µ, of at least 3000 hours. Suppose that we have reason to doubt this claim and decide to do statistical test of the claim. We choose a random sample of light bulbs manufactured by

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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BIG Corporation advertises that its light bulbs have a mean lifetime, µ, of at least 3000 hours. Suppose that we have reason to doubt this claim and decide to do statistical test of the claim. We choose a random sample of light bulbs manufactured by BIG and find that the mean lifetime for this sample 2860 hours and that the sample standard deviation of the lifetimes is 600 hours.

Based on this information, answer thi questions below.

What are the null hypothesis (H₀) and the alternative hypothesis (H₁) that should be used for the test?

H₀: µ is ____ ? _____

H₁: µ is ____ ? ____

In the content of this test, what is a Type I error?

A Type I error is ________ the hypothesis that µ is? _______ ?_______ when, in fact, µ is ? _______

Suppose that we decide to reject the null hypothesis. What sort of error might we be making? ______

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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