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Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

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BuyFindarrow_forward

Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

A population has a mean of μ = 65 and a standard deviation of σ = 16.

  • a. Describe the distribution of sample means (shape, central tendency, and variability) for samples of size n = 4 selected from this population.
  • b. Describe the distribution of sample means (shape, central tendency, and variability) for samples of size n = 64 selected from this population.

(a)

To determine

To find: The distribution of the sample means for samples of size n=4 selected from this population.

Explanation

Given info:

The population has a normal distribution with a mean of μ=65 and standard deviation of σ=16. The sample size is n=4.

Calculation:

The problem belongs to the concept of sampling distribution. The sample mean of the sampling distribution is the point estimate of the population mean and the standard error provides a measure of how much distance is expected on average between a sample mean and the population mean.

The formula for sample mean of the sampling distribution is,

μx¯=μ

The formula for standard deviation of the sampling distribution is,

σM=σn

The sample mean of the sampling distribution is,

μx¯

(b)

To determine

To find: The distribution of the sample means for samples of size n=64 selected from this population.

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