Variant 4

The size of items which were made on a factory is =35millimeters. We tested 20 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	34.8	34.9	35.0	35.1	35.3
ni	2	3	4	6	5

We weighted 10 samples of a chemical substance on two scales. We got the following results:

xi	25	30	28	50	20	40	32	36	42	38
yi	27	32	24	53	29	44	32	39	41	38

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

We approve a production lot if a probability of an item to be damaged is not bigger then 0.02. We selected randomly 600 items and found 40 defected ones. Is it possible to approve a lot (use confidence level 0.05)?

Using four independent samples with volumes 14,30,20,16 items correspondingly selected from normal universal sets we found corrected sampling variances: 0.52, 0.84, 0.76, 0.69. Using a confidence level 0.05 verify a null hypothesis on homogeneity of variance

X is normally distributed. Sample volume n=50, sampling average =22, the corrected standard deviation s=3.2. Estimate the unknown mean using confident intervals. Reliability =0.95.

Varian 5

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: =37.7. We need to verify the null hypothesis =37 using competing hypothesis and confidence level α=0.05.

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	71	57	49	70	69	26	65	59
yi	81	85	52	52	70	63	33	83	62

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=0.2, when a competing hypothesis is p<0.2.

Using four independent samples with volumes 17,20,15,16 items correspondingly selected from normal universal sets we found corrected sampling variances: 2.5, 3.6, 4.1, 5.8. Using a confidence level 0.01 verify a null hypothesis on homogeneity of variance

X is normally distributed. Sample volume n=40, sampling average =12, the corrected standard deviation s=1.2. Estimate the unknown mean using confident intervals. Reliability =0.95.