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Math 203_Lecture 11

# Math 203_Lecture 11 - Principles of Statistics 1 Lecture 11...

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Principles of Statistics 1 Lecture 11: Math 203 Abbas Khalili Department of Mathematics and Statistics McGill University May 18, 2011 Principles of Statistics 1 Lecture 11: Math 203 – p. 1/3

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Chapter 8 Tests of Hypothesis Principles of Statistics 1 Lecture 11: Math 203 – p. 2/3
Introduction So far we have learned how to use sample data x 1 , x 2 , . . . , x n to estimate a parameter of a interest, such as mean ( μ ) or proportion ( p ), of a population by: Principles of Statistics 1 Lecture 11: Math 203 – p. 3/3

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Introduction So far we have learned how to use sample data x 1 , x 2 , . . . , x n to estimate a parameter of a interest, such as mean ( μ ) or proportion ( p ), of a population by: point estimate Principles of Statistics 1 Lecture 11: Math 203 – p. 3/3
Introduction So far we have learned how to use sample data x 1 , x 2 , . . . , x n to estimate a parameter of a interest, such as mean ( μ ) or proportion ( p ), of a population by: point estimate confidence interval Principles of Statistics 1 Lecture 11: Math 203 – p. 3/3

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Introduction So far we have learned how to use sample data x 1 , x 2 , . . . , x n to estimate a parameter of a interest, such as mean ( μ ) or proportion ( p ), of a population by: point estimate confidence interval In addition to these, we may also be interested in making an inference about how the value of a parameter, e.g. μ or p , is related to a specific numerical value. Principles of Statistics 1 Lecture 11: Math 203 – p. 3/3
Examples 1. An insurance company is reviewing its current policy rates. They are concerned that the true average claim amount is actually higher than what they originally set, which was \$1 , 800 . Principles of Statistics 1 Lecture 11: Math 203 – p. 4/3

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Examples 1. An insurance company is reviewing its current policy rates. They are concerned that the true average claim amount is actually higher than what they originally set, which was \$1 , 800 . 2. The maker of a certain model car claimed that his car averaged at least 31 mpg. A sample of 9 cars showed a mean of ¯ x = 29 . 43 miles with a s = 3 miles. what do you conclude about the manufacturers claim? Principles of Statistics 1 Lecture 11: Math 203 – p. 4/3
Examples 1. An insurance company is reviewing its current policy rates. They are concerned that the true average claim amount is actually higher than what they originally set, which was \$1 , 800 . 2. The maker of a certain model car claimed that his car averaged at least 31 mpg. A sample of 9 cars showed a mean of ¯ x = 29 . 43 miles with a s = 3 miles. what do you conclude about the manufacturers claim? 3. A manufacturer company claims that in a lot of 1500 items produced by them only about 0 . 5% of the items are bad (do not work properly). You as a consumer want to investigate their claim whether it is true or not. Principles of Statistics 1 Lecture 11: Math 203 – p. 4/3

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Hypothesis testing So, in general, we would like to answer questions like: Is the value of μ (or p ) less than, equal to, or greater than a specified value?
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Math 203_Lecture 11 - Principles of Statistics 1 Lecture 11...

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