Variant 11

Date: 2015-10-07; view: 480.

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

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:

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 g=0.95.