Test of hypothesis

Question

Can you help for solving this question.What ı will use to solve this problem.I try to do something but ı thınk not correct.ı have an exam please help me

Answer 1

above 2 answer is wrong!, since that is identical trial which is only repeated measure from 7 times shoot with the same treatment, hence why both of u used $x^2$ test and $F$ test?

Hint: Remember repeated measure from 7 times shoot with the same treatment is an identical, so that we can assume and u can check the normality, which is normally independent. ($iid$) hence you should used $t$-test for 1 independent sample.

Answer 2

Let $\sigma_1^{2}=30$ meters $=$ Population variance of "Hawk" type army rockets.

$\sigma^{2}=$ Population variance of "Owl" type army rockets.

$n=7$

Calculating the sample standard deviation of the "Owl" rocket tests, we get

$S=\sqrt\frac{\Sigma (x-\overline{x})^2}{n-1}=\sqrt\frac{6^2+5^2+3^2+4^2+3^2+6^2+5^2}{7-1}=\sqrt{26}$

$H_0:\sigma^{2}=30$

$H_1:\sigma^{2}<30$

Now we calculate chi squared value $\chi^2=\frac{(n-1)S^2}{\sigma_1^{2}}=5.2$

And we have $\chi_{critical}^2\approx12.592$ at $\nu=n-1=6$ and $\alpha=0.05$

Since $\chi^2<\chi_{critical}^2$ we fail to reject $H_0$ and hence there is no strong evidence to conclude that "Owl" rockets are more accurate than "Hawk" rockets.