Question

Hemoglobin(g percent) values were recorded for a sample of 20 children who were part of a study of acute leukemia. The varience of the observation is 5 test the hypothesis if this data provide sufficient evidence to indicate that the population varience is greater than 4?

Answer 1

We define the null hypothesis and alternative hypothesis as below

H₀ : variance = 4 ( null hypothesis)

H₁ : variance > 4 (alternative hypothesis)

we use chi-square test =( (n - 1) * ( 5/4) )

This becomes ( (20- 1) * (1.25) ) =( (19) * (1.25) ) =23.75

Taking a 0.05 level of significance, the critical value at ( n-1) degrees of freedom which is (20 -1) = 19 degrees of freedom is 30.14 and the p value = 0.2059

since p = 0.2059 > 0.05 we fail to reject the null hypothesis

Hence we may conclude that the data does not support the assumption that the variance is greater than four.