Question

1. Calculate the test statistic to compare the variance in poverty rates for rural counties to that of urban cities in 2016.

2. Calculate the p-value of the test statistic to compare the variance in poverty rates for rural counties to that of urban counties in 2016.

These are two questions I have for my homework, I have an excel sheet to work with and I just need to know the operations to derive these calculations. Also, is the F-Statistic the test statistic?

Answer 1

Population 1 : poverty rates for rural counties in 2016

Population 2 : poverty rates for urban cities in 2016

: variance in poverty rates for rural counties in 2016

: variance in poverty rates for urban cities in 2016

Null hypothesis : Ho :

Two tailed : Alternate hypothesis : Ha :

Left tailed : Alternate hypothesis : Ha :

Right tailed : Alternate hypothesis : Ha :

n1 : Sample Size of Sample from rural counties

n2 : Sample Size of Sample from urban cities

s1 : Sample Standard deviation of Sample 1

s2 : Sample Standard deviation of Sample 2

Degrees of Freedom : Numerator : n1-1;

Degrees of Freedom : Denominator : n2 -1;

Two Tailed Test:

Left tailed test:

Right tailed test

Excel function to calculate

Yes the test statistic is F-Statistic.

F.DIST.RT function

This article describes the formula syntax and usage of the F.DIST.RT function in Microsoft Excel.

Returns the (right-tailed) F probability distribution (degree of diversity) for two data sets. You can use this function to determine whether two data sets have different degrees of diversity. For example, you can examine the test scores of men and women entering high school and determine if the variability in the females is different from that found in the males.

Syntax

F.DIST.RT(x,deg_freedom1,deg_freedom2)

The F.DIST.RT function syntax has the following arguments:

• X     Required. The value at which to evaluate the function.

• Deg_freedom1     Required. The numerator degrees of freedom.

• Deg_freedom2     Required. The denominator degrees of freedom.