Question

Using the data from the previous question on LDL cholesterol, you decide to test if the variance in LDL cholesterol of patients admitted to the hospital with a heart attack is the same as that of those who have not (the control). You use the R function var.test and obtain the following output.

   F test to compare two variances

data:  ldl.ha and ldl.cont

F = 7.683, num df = 9, denom df = 15,
   p-value = 0.0006501

alternative hypothesis: true ratio of
variances is not equal to 1

95 percent confidence interval:

2.460444 28.960945

sample estimates:

ratio of variances

          7.683258

What is your decision and conclusion (with respect to variation in LDL cholesterol levels) from the above R test output assuming an alpha level of 0.05? AND how does this help us beyond this test of the variance?

Answer 1

We want to test that the he variance in LDL cholesterol of patients admitted to the hospital with a heart attack is the same as that of those who have not (the control).

Ho:- The variance in LDL cholesterol of patients admitted to the hospital with a heart attack is the same as that of those who have not (the control).

Vs

Ha:- The variance in LDL cholesterol of patients admitted to the hospital with a heart attack is different from those who have not (the control)

Here from output decision based on P-value.

Alpha = level of significance = 0.05

P-value = 0.0006501

Reject Ho if P-value < alpha

Here p-value = 0.0006501 < alpha = 0.05

So we reject Ho

So we conclude that the The variance in LDL cholesterol of patients admitted to the hospital with a heart attack is different from those who have not (the control)

So variances are unequal.

This decision can be used in testing of difference between the two population means where we want to know that population variances are equal or not.