Question

Bonus problem (6 points:) Assume X1, ... Xm come from a normal population with unknown variance oị and Y... Y come from another normal population with unknown variance o, and the two samples are independent of each other. Write the 5 steps you will follow to test the hypotheses: Hoi = 1 VS HQI # 1 Make sure to specify the test statistic and the null distribution (don't forget the degrees of freedom), and the rejection region. Hint: Remember that i x , and 2-X-. What do we get when we have the ratio of two chi-square random variables? Be careful on the rejection region. F distribution is not symmetric (similar to the chi-square distribution). So, the idea of the two critical points should be as the one we used for chi-square critical points.

Answer 1

here i have written the five steps to solve the problem . the steps are

a. calculate sample variences

b. distributions of sample variences

c. construct test statistic.

b. calculate and observe the tabulated value of test statistic.

c. find critical region.

there, Assume, X1, X2, ... xm come from a normal population with unknown varience or and Y2Y2, ..., Yn come from the norma populotoy Нth и К сини у ло 0, We have to tast, Ho: 02/02 & 1 vs He: 8/281. 2 Step 1: Here the population variences to are Ол KyrІЧА, then, we have to estimate them beg calculating sample varience. E(82) = or cirros Now, the formular for sample varience is & I [hi-X S n-1 Here si and s2 are sample variences for two samples.

m and. lai-n). Savanese slai ā). Se 7 m-1 izle t it sus step I We have to know the distribution of sample varience. We know that, & cai-ngnxo n and S (x-7) ~ Km 121

Do monstNBTS do you "! ni's are coming from normal popeilation for both the samples. then, Ma - 1 st nyt and (m-1) s km.

Steps Constracting statistie, Now, we will construct the F statistie, to tener la o to 82 E ~ Fn-m-18th of 82 n-1) 1 M-101 Form (m-1) S7 / m- 1882 . Stad we have to calculate the value of F.

Step 4 . Now, the two tailed critical region for test in F distribution is veritical region A02 y britical region. So, let, d=0.05, [= significant rever] then, a/2 = 0.025. Now, Here we observe the tabulated value of F0.025, n-l, m-1. and F,-0.025, 1-1, mil. steps if the observed / calculated rative fni, m-1 <F 1-0.025, n-2m- or Fn-hm- , 7 F0.025, 8-12m.I. o we regect the null hypotheses.