Variant 6

We select a sample with volume n=35 from a normal universal set. The standard deviation is is known: σ=20. We find sampling average: =210. We need to verify the null hypothesis =200 using competing hypothesis and confidence level 0.01.

A laboratory made an analysis of 8 samples using 2 methods. The results are shown in the table.

xi	15	20	16	21	24	12	18	20
yi	10	24	12	28	19	11	21	22

Using confidence level 0.01 verify, if the measurements results differ significantly (we suppose them to be distributed normally)

After 1000 independent tests we found relative frequency 0.33. Using confidence level 0.05 verify a hypothesis: p=0.3, when a competing hypothesis is p>0.3.

Using three independent samples with volumes 19,13,15 items correspondingly selected from normal universal sets we found corrected sampling variances: 3.1, 3.8, 6.2. Using a confidence level 0.05 verify a null hypothesis on homogeneity of variance

X is normally distributed. Sample volume n=55, sampling average =17, the corrected standard deviation s=0.5. Estimate the unknown mean using confident intervals. Reliability =0.95.

Variant 7

We select a sample with volume n=40 from a normal universal set. The standard deviation is known: σ=40 We find sampling average =99. We need to verify the null hypothesis =100 using competing hypothesis .and confidence level 0.01

The level of physical form of 9 sportsmen is measured in points. Sportsmen were tested twice with a 1-month interval. The testing results are presented in a table:

xi	76	73	57	42	70	69	26	70	59
yi	80	85	53	58	81	64	40	83	66

Using confidence level 0.05 verify, if the testing results differ significantly (we suppose them to be distributed normally)

After 100 independent tests we found relative frequency 0.14. Using confidence level 0.05 verify a hypothesis: p=0.1, when a competing hypothesis is p0.1.

Using four independent samples with volumes 77,90,85,76 items correspondingly selected from normal universal sets we found corrected sampling variances: 3.5, 3.7, 4.2, 5.1. Using a confidence level 0.01 verify a null hypothesis on homogeneity of variance

X is normally distributed. Sample volume n=40, sampling average =10, the corrected standard deviation s=1.2. Estimate the unknown mean using confident intervals. Reliability =0.95.

Variant 8

The size of items which were made on a factory is =45millimeters. We tested 18 items that were selected randomly (data are presented in a table). Using confidence level 0.05, verify if there is a common deviation in a selected item set.

xi	44.1	44.9	45.2	45.4	45.9
ni	1	3	6	6	2

A laboratory made an analysis of 8 samples using 2 methods. The results are shown in the table.

xi	15	20	16	22	24	14	18	20
yi	15	22	14	25	29	16	20	24

Using confidence level 0.01 verify, if the measurements results differ significantly (we suppose them to be distributed normally)

After 100 independent tests we found relative frequency 0.14. Using confidence level 0.05 verify a hypothesis: p=0.15, when a competing hypothesis is p<0.15.

Using three independent samples with volumes 19,23,35 items correspondingly selected from normal universal sets we found corrected sampling variances: 4.2, 3.8, 6.3. Using a confidence level 0.05 verify a null hypothesis on homogeneity of variance

X is normally distributed. Sample volume n=35, sampling average =5, the corrected standard deviation s=0.2. Estimate the unknown mean using confident intervals. Reliability =0.95.