The flow of water through soil depends on the porosity of the soil which is assumed to be normally distributed. To compare two types of 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 two sample variances

S₁²=0.01 and S₂²=0.02.

1. (a) construct 95% two sided confidence interval for ratio of variance2/variance1. Is there any evidence that two populations variances are equal.
2. Find the probability that the difference the sample means will be within 0.005. Use the result from (1) to decided whether a pooled variance should be used.
3. If the difference of sample means is 0.03( X-Y=0.03) Construct a 95% confidence interval for the difference of population means.Use the result in (1) to decide whether a pooled variance should be used.