Variant 1

Date: 2015-10-07; view: 386.

We select a sample with volume n=100 from a normal universal set. The standard deviation is known: σ=5.2. We find sampling average: =27.56. We need to verify the null hypothesis =26 using competing hypothesis and confidence level α=0.05.

We measured 6 items using two devices and got the following results:

Using the confidence level 0.05 verify, if the measurements results differ significantly (we suppose the size of item is distributed normally)

We approve a production lot if a probability of an item to be damaged is not bigger then 0.03. We selected randomly 100 items and found 18 defected ones. Is it possible to approve a lot (use confidence level 0.05).

Using four independent samples with volumes 25,33,29,33 items correspondingly selected from normal universal sets we found corrected sampling variances: 0.05, 0.07, 0.10, 0.08. Using a confidence level 0.05 verify a null hypothesis on homogeneity of variance

X is normally distributed. Sample volume n=16, sampling average =20.2, the corrected standard deviation s=0.8. Estimate the unknown mean using confident intervals. Reliability g=0.95.