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Statistics for The Behavioral Scie...

10th Edition
Frederick J Gravetter + 1 other
ISBN: 9781305504912

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Section
BuyFindarrow_forward

Statistics for The Behavioral Scie...

10th Edition
Frederick J Gravetter + 1 other
ISBN: 9781305504912
Textbook Problem

The following sample of n = 4 scores was obtained from a population with unknown parameters.

Scores: 2, 2, 6, 2

a. Compute the sample mean and standard deviation. (Note that these are descriptive values that summarize the sample data.)

b. Compute the estimated standard error for M . (Note that this is an inferential value that describes how accurately the sample mean represents the unknown population mean.)

To determine

Sample mean, standard deviation and estimated standard error of the sample mean from the sample.

Explanation

Given:

n=4, sample values = 2,2,6,2

Formula used:

a) For calculating sample mean(M) we simply need to do calculation without any second thought, and the same is true for calculating sample standard deviation.

Sample Mean (M) = 1ni=1nXi Sample standard deviation = 1n1i=1n(XiX¯)2

b ) The formula for standard error for sample mean(M) is available in generalized case, in terms of population variance, considering the population variance is known if it is not known we use its estimate based on the sample. The best estimate of population variance is sample mean square which is the square of sample standard deviation.

S.E (M) = σ^Xn Where σ^X = 1n1i=1N(XiX¯)2 i

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