Variant 1

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:

xi	2	3	5	6	8	10
yi	10	3	6	1	7	4

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 =0.95.

Variant 2

We select a sample with volume n=64 from a normal universal set. The standard deviation is known: σ=40. We find sampling average: =136,5. We need to verify the null hypothesis =130 using competing hypothesis and confidence level 0.01.

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	28	31	26	52	24	36	33	35	45	40

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 0.03. We selected randomly 250 items and found 28 defected ones. Is it possible to approve a lot (use confidence level 0.05).

Using four independent samples with volumes 15,20,20,14 items correspondingly selected from normal universal sets we found corrected sampling variances: 0.53, 0.78, 0.96, 0.62. Using a confidence level 0.05 verify a null hypothesis on homogeneity of variance

X is normally distributed. Sample volume n=36, sampling average =10.1, the corrected standard deviation s=0.3. Estimate the unknown mean using confident intervals. Reliability =0.95.

Variant 3

We select a sample with volume n=64 from a normal universal set. The standard deviation is known: σ=50 We find sampling average =146,5. We need to verify the null hypothesis =150 using competing hypothesis .and confidence level 0.01

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

xi	2	3	5	6	8	10
yi	1	4	8	9	8	6

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 0.02. We selected randomly 480 items and found 12 defected ones. Is it possible to approve a lot? (use confidence level 0.05).

Using four independent samples with volumes 28,34,30,31 items correspondingly selected from normal universal sets we found corrected sampling variances: 0.03, 0.17, 0.11, 0.02. Using a confidence level 0.05 verify a null hypothesis on homogeneity of variance

X is normally distributed. Sample volume n=26, sampling average =25, the corrected standard deviation s=1.8. Estimate the unknown mean using confident intervals. Reliability =0.95.