# Definition and Description of Statistics

Define / describe in your own words the following terms and give an example of each.

a. F distribution

b. F statistic

c. Chi-square distribution

d. T distribution

e. Dependent samples

f. Independent samples

g. Degrees of freedom

h. T statistic

i. Paired difference

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Define / describe in your own words the following terms and give an example of each.

a. F distribution

b. F statistic

c. Chi-square distribution

d. T distribution

e. Dependent samples

f. Independent samples

g. Degrees of freedom

h. T statistic

i. Paired difference

Solution:

a. F distribution:

The F distribution is defined by F =[ U/n1]/[V/n2], where U and V are independent chi square variables with n1 and n2 degrees of freedom respectively. Thus if independent random samples of size n1 and n2 respectively are taken from normal populations with variances 1^2 and 2^2 then

S1²/1²/S2²/2² F n1-1,n2-1

b. F statistic:

Here are the steps required to compute an f statistic:

• Select a random sample of size n1 from a normal population, having a standard deviation equal to σ1.

• Select an independent random sample of size n2 from a normal population, having a standard deviation equal to σ2.

• The f statistic is the ratio of s12/σ12 and s22/σ22.

The following equivalent equations are commonly used to compute an f statistic:

f = [ s12/σ12 ] / [ s22/σ22 ]

f = [ s12 * σ22 ] / [ s22 * σ12 ]

f = [ Χ21 / v1 ] / [ Χ22 / v2 ]

f = [ Χ21 * v2 ] / [ Χ22 * v1 ]

where σ1 is the standard deviation of population 1, s1 is the standard deviation of the sample drawn from population 1, σ2 is the standard deviation of population 2, s2 is the standard deviation of the sample drawn from population 2, Χ21 is the chi-square statistic for the sample drawn from population 1, v1 is the degrees of freedom for Χ21, Χ22 is the chi-square statistic for the sample drawn from population 2, and v2 is the degrees of freedom for Χ22 . Note that degrees of freedom v1 = n1 - 1, and degrees of freedom v2 = n2 - 1 .

Suppose you randomly select 7 women from a population of women, and 12 men from a population of men. The table below shows the ...

#### Solution Summary

The definition and description of statistic terms are discussed.