Variant 10

Date: 2015-10-07; view: 452.

There are two independent samples with the volumes . They have been extracted from the normal universal sets X,Y. The corrected sampling variances have been found: . The confidence level α=0.1. Verify the following null hypothesis . The competing hypothesis is .

We select a sample of volume n=17 from a normal universal set. The corrected sampling variance =0.24. We need to verify the null hypothesis . The confidence level is 0.05. The competing hypothesis is: .

The average size of items made on the 1^st lathe equals x=20.1mm. (sample volume n=50). The average size of items made on the 2^nd lathe equals y=19.8mm. (sample volume n=50). Universal variances are known: D(X)=1.75 mm², D(Y)=1.375 mm². 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 need to verify a null hypothesis for normal universal sets X,Y using the competing hypothesis . The confidence level is 0.05. The sampling data are following:

X is normally distributed. Sample volume n=100, sampling average =25, the corrected standard deviation s=2. Estimate the unknown mean using confident intervals. Reliability g=0.95.