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AP®︎/College Statistics

Course: AP®︎/College Statistics > Unit 9

Lesson 7: Sampling distributions for differences in sample means

Mean and standard deviation of difference of sample means

A car manufacturer has two production plants in different cities. Every day, plant A produces 120 of a certain type of car, while plant B produces 80 of those cars. On average, all of these cars have a paint thickness of 0, point, 04, start text, m, m, end text with a standard deviation of 0, point, 003, start text, m, m, end text.

Every day, quality control experts take separate random samples of 10 cars from each plant and calculate the mean paint thickness for each sample. They then look at the difference between those sample means.

Consider the formula:

sigma, start subscript, x, with, \bar, on top, start subscript, 1, end subscript, minus, x, with, \bar, on top, start subscript, 2, end subscript, end subscript, equals, square root of, start fraction, sigma, start subscript, 1, end subscript, squared, divided by, n, start subscript, 1, end subscript, end fraction, plus, start fraction, sigma, start subscript, start text, 2, end text, end subscript, squared, divided by, n, start subscript, 2, end subscript, end fraction, end square root

Why is it not appropriate to use this formula for the standard deviation of x, with, \bar, on top, start subscript, start text, A, end text, end subscript, minus, x, with, \bar, on top, start subscript, start text, B, end text, end subscript?

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AP®︎/College Statistics

Course: AP®︎/College Statistics > Unit 9

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