Question

An F-statistic is:

	a.	the ratio of two variances
	b.	a population parameter
	c.	the variance of the difference between means
	d.	a ratio of two means
	e.	the difference of standard deviations

The characteristics of the F-Distribution include all but:

	a.	it is positively skewed
	b.	it is symmetrical much like the normal distribution
	c.	its value can never be negative
	d.	there is a family of distributions dependent upon the degrees of freedom
	e.	it is continuous

Which statement about the F-distribution is correct:

	a.	it is the same as the t-distribution.
	b.	It is always between -1 and +1.
	c.	It is always between 0 and 1.
	d.	It increases toward infinity as the degrees of freedom increase.
	e.	It cannot be negative.

Analysis of Variance is used to:

	a.	compare nominal data.
	b.	compare population proportions.
	c.	simultaneously compare several population means.
	d.	calculate an normal probability.
	e.	compute the t test.

Answer 1

Q1) An F statistic is the ratio of variances. Usually a random variable which follows a F distribution can be expressed as the ratio of 2 independent chi squared distribution divided by their respective degrees of freedom. The F statistic plays important role in testing significance of regression. In this case F statistic is the ratio of restricted sum of squares under null hypothesis and unrestricted sum of squares also called SSE ( Error sum of squares ) divided by their respective degrees of freedom.

Q2) F distribution is not symmetric like normal distribution since the skewness depends on the degrees of freedom of the F distribution. Since it is the ratio of 2 independent chi square distribution its value is always positive. The family of distributions depend on the degrees of freedom of the distribution. F distribution is continuous.

Q3) The F distribution cannot take any negative value since it is the ratio of 2 independent chi square distribution and chi square distribution is the sum of square of standard normal random variables so positive. The range of F distribution is from 0 to infinity and it is independent of the values of degrees of freedom. The range of t distribution is from minus infinity to plus infinity. So option e is correct

Q4) Analysis of variance is used to compare simultaneously several population means. Consider the model

i =1 ,2,3, 4. j= 1,2,..., n

where are iid N(0,1) random variables.

Then to test H0 : is done using Analysis of Variance.