Answer to Question #293124 in Statistics and Probability for Emu

Question

Studied nine subjects who underwent baffle procedure for transposition of greater artery.at baseline the systemic vascular resistant measured is WU×m2 value at rest yielded a standard deviation of 28.test the hypothesis if we can conclude from this data the SVR Varience of the population of similar subjects with TGA is not 700?

Answer 1

$n=9\\s=28\implies s^2=784\\\alpha=0.05$

The hypotheses we test here are,

$H_0:\sigma^2=700\\vs\\H_1:\sigma^2\not=700$

The test statistic is,

$\chi^2_c={(n-1)\times s^2\over \sigma^2_0}={(9-1)\times784\over700}={6272\over700}=8.96$

The critical value is, $\chi^2_{{0.05\over2},n-1}=\chi^2_{0.025,8}= 17.53455$

The null hypothesis is rejected if $\chi^2_c\gt\chi^2_{0.025,8}$

Since $\chi^2_c=8.96\lt\chi^2_{0.025,8}=17.53455$, we fail to reject the null hypothesis and conclude that there is no sufficient evidence to show that the variance of the population of similar subjects with TGA is not 700 at 5% level of significance.