Question

Hemoglobin (g percent) values were recorded for a sample of 20 children who were part

of a study of acute leukemia. The variance of the observations was 5. Do these data

provide sufficient evidence to indicate that the population variance is greater than 4?

α=5

Answer 1

$n=20\\s^2=5$

Hypotheses,

$H_0:\sigma^2=4\\vs\\H_1:\sigma^2\gt 4$

The test statistic is,

$\chi^2_c={(n-1)\times s^2\over \sigma^2}={19\times5\over4}=23.75$

The critical value is ,

$\chi^2_{\alpha,n-1}=\chi^2_{0.05,19}=30.1435$

Reject the null hypothesis if, $\chi^2_c\gt\chi^2_{0.05,19}$.

Now, $\chi^2_c=23.75\lt\chi^2_{0.05,19}=30.1435$ therefore, we fail to reject the null hypothesis and conclude that these data do not provide sufficient evidence to indicate that the population variance is greater than 4 at 5% significance level.