The table below consists of two data samples (X and Y). Please conduct a test fo
ID: 3264774 • Letter: T
Question
The table below consists of two data samples (X and Y). Please conduct a test for the equality of the population variances of the two populations from which these samples are drawn. Please use 90% significance level in your test. Please state the results of the test below.
X
A.
A. The test REJECTS the hypothesis that the two population variances are equal
B. The test FAILS TO REJECT the hypothesis that the two population variances are equal
C. Not enough information is presented to conduct the test
X
Y 36 42 34 46 32 45 35 50 33 44 33 40 36 45 37 43 35 47 36 47 31 42 37 46 37 43 40 48 34 38 39 44Explanation / Answer
sol:
F test for Population variances
variance of x in excel =s1^2=5.963
variance of Y in excel=s2^2=9.317
Given sample sizes of n1n1 and n2n2, the test statistic will have n11 and n21 degrees of freedom, and is given by the following formula.
F=s1^2/s2^2=variance of X/variance of Y=5.963/9.317=0.640
n1-1=16-1=15
n2-1=16-1=15
critical F value=1.972
calcualted F value <critical F value
Fail to Reject null hyypothesis
. The test FAILS TO REJECT the hypothesis that the two population variances are equal
OPTIONB