In: Statistics and Probability
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.
: Population variance of number of miles traveled by Professors
: Population variance of number of miles traveled by Students
Null hypothesis : Ho : = or
Alternate hypothesis : Ho : 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.