escA researcher wishes to test if the variance of scores on a particular exam is the same for collegestudents who work full time as for college students who don't work at all. She samples the scores of47 students who work full time (group A) and the scores of 40 students who do not work (group B).She attains the following results:Group A:268.3, 259.2, 121.3, 185.9, 136.8, 220.9, 117.4, 187.8, 174.4, 123.3, 146.7, 171.2, 178.6, 124.7, 142.9,186.4, 127.9, 189.6, 184.3, 194.1, 70.7, 97.6, 155.6, 105.5, 94.8, 113.6, 25.6, 170, 137.4, 130.3, 63.9,94.4, 130.9, 159.8, 138.5, 147.4, 131.6, 146.1, 101.7, 106.1, 166.1, 128.7, 182.8, 87.9, 131, 221.4, 212Group B:240.8, 143.9, 158.6, 175.6, 144.6, 143.9, 173.4, 173.9, 182.1, 149.2, 159.5, 210.7, 133.7, 105.5, 129.6,100.6, 48.1, 199, 158.1, 147.4, 158.1, 139.9, 56.8, 164.2, 155.3, 155.3, 170.8, 108.6, 110.9, 106.6,152.8, 127.5, 142.5, 143.6, 136.1, 113.2, 131.2, 199.3, 184, 127.9Perform a hypothesis test using a 10% level of significance to test if the variance between the twogroups is different.Step 1: State the null and alternative hypotheses.35Ho:Ha:OR? V?V(So we will be performing a Select an answertest.)Part 1 of 4Submit PartXHannahFaceTime Video 01:38:082

The question is about hypo testing Given : No. of obs. under grp. A ( nA ) = 47 No. of obs. under grp. B ( nB ) = 40 To find : Test that var. between two groups is differentFirstly need to find sample var. of two groups The formula of sample var. is given by s2 = ∑ x - x¯ 2n-1Where,x¯ = ∑ xn To find : Sample var. of grp. A x¯A = 268.3 + 259.2 + .... + 21247 = 146.6596sA2 = 268.3 - 146.6596 2 + ( 259.2 - 146.6596 )2 + .... + ( 212 - 146.6596 )247-1 = 2336.781 And, To find : Sample var. of grp. B x¯B = 240.8 + 143.9 + .... + 127.940 = 146.57sB2 = ( 240.8 - 146.57 )2 + ( 143.9 - 146.57 )2 + .... + ( 127.9 - 146.57 )240-1 = 1378.171 Then, Step 1 : Null and alt. hypo. H0 : σA2σB2 = 1Ha : σA2σB2 ≠ 1 Here, need to perform F test Step 2 : The formula of test stat is given by F = sA2sB2 = 2336.7811378.171F = 1.695566 Step 3 : Since alt. hypo. has not equal to sign, so it is two tailed test firstly, need to find p value for one tailed test using excel command, =F.DIST.RT ( Test stat, nA - 1, nB - 1 ) So, p value for one tailed test is 0.046957 To find p value for two tailed test, multiplying the above value by 2 p value = 0.046957 * 2 p value = 0.093915 Step 4 : Decision rule : If p value < level of signif. ( α ) then reject H0 otherwise fail to reject H0 Given : level of signif. ( α ) = 0.10 Here, p value < α Reject H0 Step 5 : Conclusion : There is suffi. evid. to conclude that the var. between two groups are diff.