Question

Eleven students and 14 professors took part in a study to find mean commuting distances. The mean number of miles traveled by students was 5.6 and the standard deviation was 2.8. The mean number of miles traveled by professors was 14.3 and the standard deviation was 9.1. Perform a test of the null hypothesis that the population variances are equal.

Answer 1

: Population variance of number of miles traveled by  Professors

: Population variance of number of miles traveled by  Students

Null hypothesis : H_o : = or   

Alternate hypothesis : H_o : or   

Given
n1 : Sample Size of Sample 1 : number of professors took part in study	14
n2 : Sample Size of Sample 2: number of students took part in study	11
s1 : Sample Standard deviation of Sample 1: Sample standard deviation number of miles traveled by  Professors	9.1
s2 : Sample Standard deviation of Sample 2: Sample standard deviation number of miles traveled by  Students	2.8
Degrees of Freedom : Numerator : n1 -1;14-1=13	13
Degrees of Freedom : Denominator : n2 -1;11-1=10	10
Level of Significance :	5%

p-value for two tailed test :

As P-Value i.e. is less than Level of significance i.e (P-value:0.0008 < 0.05:Level of significance); Reject Null Hypothesis

There is sufficient evidence to conclude that the  the population variances are equal.