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Name: A manufacturer claims that the mean lifetime, μ, of its light bulbs is
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Description: A manufacturer claims that the mean lifetime, μ, of its light bulbs is 44 months. The standard deviation of these lifetimes is 6 months. Fifty bulbs are selected at random, and their mean lifetime is found to be 42 months. Can we conclude, at the 0.0

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.2: Expected Value And Variance Of Continuous Random Variables

Problem 10E

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A manufacturer claims that the mean lifetime, μ, of its light bulbs is 44 months. The standard deviation of these lifetimes is 6 months. Fifty bulbs are selected at random, and their mean lifetime is found to be 42 months. Can we conclude, at the 0.05 level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from 44 months?

State the null hypothesis H0 and the alternative hypothesis H1

Would the Z test be used?

Find the value of the z test?

Find the p-value?

Can we conclude that the mean lifetime of light bulbs made by this manufacturer differs from 44 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 + ...

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