Variant 11

In order to compare the accuracy of two lathes two samples have been made. Their volumes are: . The following results have been received:

1st sample (X)	1.08	1.10	1.12	1.14	1.15	1.25	1.36	1.38	1.40	1.42
2nd sample (Y)	1.11	1.12	1.18	1.22	1.33	1.35	1.36	1.38

Is it possible to suppose that the lathes have the same accuracy, if we consider the confidence level α=0.1 (the competing hypothesis lies in lathes accuracy difference).

The accuracy of a lathe is verified by variance of a product size. It must not exceed =0.1. We made a random product sample. The results are following:

Product size	3.0	3.5	3.8	4.4	4.5
Frequencies	2	6	9	7	1

We need to verify if the lathe can provide the needed accuracy. The confidence level is 0.05.

The average weight of items made on the 1^st lathe equals x=130g. (sample volume n=30). The average weight of items made on the 2^nd lathe equals y=125g. (sample volume n=40)..Universal variances are known: D(X)=60 g², D(Y)=80 g². We need to verify the following null hypothesis (confidence level is 0.05): E(X)=E(Y). The competing hypothesis is . The random variables X,Y are normally distributed, and the samples are independent.

We have two independent small samples. Their volumes are n=10, m=8, and they were selected from normal universal sets. We found sampling averages and corrected sampling variances . The confidence level is α=0.01. We need to verify the null hypothesis when the competing hypothesis is .

X is normally distributed. Sample volume n=100, sampling average =35, the corrected standard deviation s=20. Estimate the unknown mean using confident intervals. Reliability =0.95.