Question

The flow of water through soil depends on the porosity of the soli which is assumed to be normally distributed. To compare two types of sandy soil n₁=16 measurements are to be taken on the porosity of soil A and n₂=21 measurements are to be taken on soil B Assume that the two sample variances S₁²= 0.01,  S₂²= 0.02.

(a) construct a 95% confidence interval for ratio of variances. Is there any evidence that two population variances are qual.

(b) Find the probability that the difference between the sample  means will be within 0.005 units of the difference between the population means. Use the result in (a) to decide whether a pooled variance should be used.

(c)If $\overline{X} - \overline{Y}=0.03$ . Construct 95% confidence interval for difference of population means. Use the results in (a) to decide whether a polled variance should be used.

Answer 1

3) Griven data is that sn=0.01 n, -16 Sq2 = 0.02. 12-21 95 cc. I for rario we need to construct ob variances, o for this we need to have a test statistic. which is E X-1/n - Suur en n Ral susir is here we introduce Xalnet pivotal quantity two constant F . 2 Fri, del, prala & Miri, Azt gf 2 such that VI hal, n₂-1, 2/2 nirl ₂ 1 / 2 calculation: n. 1, 12-1), ale 1-25 0.95 % = 0.025 -&- v.95 (-09) 20.25 - 0.25 OZ tis, 20, 0.025 = 2.5731 - esi = 0.3886 Fis, 20, 0.025 2.5731 otr aig72, 0.6933 T There is enough J. evidence or tour PC So

- The language of The language of this sentence is not understandable ib it is like that then find the value of dy from here H,- H< 3- 7 sort the thing nith 2 a nere pooled rowance Spi risanie s poble n+n,- 2 Campo oroos - Set mith - 2 a bind d. But But here here so is not needed as a so is not (©), Now we need to find the 95 '. c. I ob Mir Me as we have seen in a that I # 1 from that Co so, we consider ortretoria Hence our test tests statistic would be %-%- (Mith) Thitn, -2 n2 To bind the 95 7. c. I sex-Tasche te Min - 2 S 22 > Mi-Po e x-F Emin -2,062 calculation: M-HÉ 0,03 F 20301X0.005 = [0, 018, 0.0427
there might be a mistake for question b. And why we are taking population variances are unequal. Because we saw this first confidence interval does not include 1. Only when the ratio of population variances is 1 then we can say they are equal. But here we didn't see such condition. So we don't need to take pooled variance. Rather take separate sample variances what I did here. Check the calculations and follow the method.