Download F Distribution: Arises when we have ratios of quantities. F test

Hypothesis Testing...We've come a long way.
TYPE
Tests for Means:
TEST STATISTIC
Large Sample
Small Sample
Two Large Samples
Two Small Samples
Tests for Proportions:
Large Sample
Test for Goodness of Fit:
Multinomial Trial
Test for Independence:
Contingency Table
Two Variable
Test for Equal Variances:
Two Samples From
Normal Populations
F Distribution: Arises when we have ratios of quantities.
F test statistics are > 0
The F distribution curve differs for changing sample sizes.
Numerator degrees of freedom = nx ­ 1
Denominator degrees of freedom = ny ­ 1
How to use a F distribution table:
Using the table is not as accurate as using the Fcdf feature of your calculator.
Fcdf(low, high, num df, denom df)
With the F Test we can test to see if...
two samples come from populations with equal variances.
a new process, treatment, or test reduces the variability compared to the current process.
The two populations MUST be normal. This test is highly sensitive to departures from normality. Example: Under various environmental conditions, two computer models predicted surface temperature. Errors in the predictions were recorded for both. Assuming the errors are normally distributed, is there evidence to show the population variances are not the same?
x = 1.99 sx = 0.057
nx = 8
y = 2.03
sy = 0.021
ny = 7
Double the probability in the tail since this is a two tailed test.
For the SAME temperature data. Is there evidence that the mean errors are different?
x = 1.99 sx = 0.057
nx = 8
y = 2.03
sy = 0.021
ny = 7
We know we would need a t statistic since we have small samples and normal populations but should we pool or not pool? We should NOT since the F test showed us that the population variances were not equal.
Example: Meat, meat byproducts, and other ingredients are mixed to produce pet food. A floor manager at a pet food production company suspects that one production line is filling cans with a larger variation compared to another production line. Is there evidence that the variance in production line X is greater than production line Y?
Notice...
Ho: σx2 = σy2 H1: σx2 ≠ σy2 If we reject Ho...
If we fail to reject Ho...we do NOT conclude that the variances are equal. We never can conclude the null hypothesis is true.
Be sure to read page 467.