Chapter 6: Q3 (page 272)

Notation In general, what do the symbols $μ_{\bar{x}}$ and $σ_{\bar{x}}$ represent? What are the values of $μ_{\bar{x}}$ and $σ_{\bar{x}}$ for samples of size 64 randomly selected from the population of IQ scores with population mean of 100 and standard deviation of 15?

Short Answer

Expert verified

Symbols:

$μ_{\bar{x}}$ represents the mean value of all sample means.

$σ_{\bar{x}}$ represents the standard deviation of all the sample means.

For the given values of sample size and population parameters, the values of $μ_{\bar{x}}$ and $σ_{\bar{x}}$ are as follows:

$μ_{\bar{x}} = 100$
$σ_{\bar{x}} = 1.875$

Step by step solution

Given information

It is given that 64 random samples have been considered from the population of IQ scores with a population mean equal to 100 and population standard deviation equal to 15.

Notations

The symbol $μ_{\bar{x}}$ denotes the mean value of all sample means.

The symbol $σ_{\bar{x}}$ denotes the standard deviation of all the sample means.

Here, the value of the population mean is equal to: $μ = 100$

The value of the population standard deviation is equal to: $σ = 15$

The sample size (n) is equal to 64.

The values of $μ_{\bar{x}}$ and $σ_{\bar{x}}$ are computed below:

$μ_{\bar{x}} = μ = 100$

$σ_{\bar{x}} = \frac{σ}{\sqrt{n}} = \frac{15}{\sqrt{64}} = 1.875$

Therefore, the value of $μ_{\bar{x}}$ is equal to 100 and the value of $σ_{\bar{x}}$ is equal to 1.875.

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Notation In general, what do the symbols $μ_{\bar{x}}$ and $σ_{\bar{x}}$ represent? What are the values of $μ_{\bar{x}}$ and $σ_{\bar{x}}$ for samples of size 64 randomly selected from the population of IQ scores with population mean of 100 and standard deviation of 15?

Short Answer

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Notation In general, what do the symbols μx¯ and σx¯ represent? What are the values of μx¯and σx¯for samples of size 64 randomly selected from the population of IQ scores with population mean of 100 and standard deviation of 15?

Short Answer

Step by step solution

Given information

Notations

One App. One Place for Learning.

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Notation In general, what do the symbols $μ_{\bar{x}}$ and $σ_{\bar{x}}$ represent? What are the values of $μ_{\bar{x}}$ and $σ_{\bar{x}}$ for samples of size 64 randomly selected from the population of IQ scores with population mean of 100 and standard deviation of 15?