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OlgaM077 [116]
3 years ago
11

A researcher obtained M = 27 for a sample of n = 36 scores selected from a population with µ = 30 and σ = 18. This sample mean c

orresponds to a z-score of z = –1.00.
Mathematics
1 answer:
dusya [7]3 years ago
7 0

Answer:

True

Step-by-step explanation:

Given that:

M = 27, sample of n = 36 scores, µ = 30 and σ = 18.

The z score is used in statistics to determine by how many standard deviations the raw score is above or below the mean. If the z score is positive, the raw score is greater than the mean and if the z score is negative the raw score is less than the mean. The z score is given as:

z=\frac{x-\mu}{\sigma}

Given that M = 27, this means that x = 27. Therefore:

z=\frac{x-\mu}{\sigma}\\\\for \ a\ sample\ size(n):z=\frac{x-\mu}{\sigma/\sqrt{n} }\\\\z=\frac{27-30}{18/\sqrt{36} } =\frac{-3}{3}=-1

This sample mean corresponds to a z-score of z = –1.00.

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