If one wants to convert random numbers selected from two digit numbers 00-99 to uniformly distributed U (0, 1) variables then one has to divide them by 99.
By generating 10 uniform random variate U (0, 1) estimate the integral
Recognizing this function as probability density function of N (0,1), compare the value of with
.
An experiment was planned to study the effect of Sulphate, Potash and Super Phosphate on the yield of potatoes. All the combinations of 2 levels of Super Phosphate [0 cent (p0) and 5 cent (p1)/ acre] and two levels of Sulphate and Potash [0 cent (k0) and 5 cent (k1)/acre] were studied in a randomised block design with 4 replications each. The (1/70) yields [lb per plot = (1/70) acre] obtained are given in table below:
| Blocks | Yields (lbs per plot) | |||
| I | (1) 23 | k 25 | p 22 | kp 38 |
| II | p 40 | (1) 26 | k 36 | kp 38 |
| III | (1) 29 | k 20 | pk 30 | p 20 |
| IV | kp 34 | k 31 | p 24 | (1) 28 |
Analyse the data and give your conclusions.
To determine the yield rate of wheat in a district of Punjab, 6 groups were constructed of 6 plots each. The data is given in the following table:
| Plot No. | Group 1 | Group 2 | Group 3 | Group 4 | Group 5 | Group 6 |
| 1 | 8 | 6 | 18 | 13 | 17 | 12 |
| 2 | 13 | 5 | 8 | 7 | 15 | 15 |
| 3 | 11 | 16 | 6 | 13 | 10 | 11 |
| 4 | 26 | 5 | 10 | 6 | 21 | 17 |
| 5 | 13 | 16 | 16 | 7 | 20 | 8 |
| 6 | 31 | 5 | 20 | 2 | 25 | 10 |
Select a cluster sample of 3 clusters from the given data and find sample mean.
In SRSWOR, the possible numbers of sample of size n from a population of size N if sampling is done with replacement is Nn .
In a class of Statistics, total number of students is 30. Select the linear and circulur systematic random samples of 10 students. The age of 30 students is given below:
| age | 22 | 25 | 22 | 21 | 22 | 25 | 24 | 23 | 22 | 21 | 20 | 21 |
| 22 | 23 | 25 | 23 | 24 | 22 | 24 | 24 | 21 | 20 | 23 | 21 | 22 |
| 20 | 20 | 21 | 22 | 25 |
b) To determine the yield rate of wheat in a district of Punjab, 6 groups were constructed of 6 plots each. The data is given in the following table:
| Plot No. | Group 1 | Group 2 | Group 3 | Group 4 | Group 5 | Group 6 |
| 1 | 8 | 6 | 18 | 13 | 17 | 12 |
| 2 | 13 | 5 | 8 | 7 | 15 | 15 |
| 3 | 11 | 16 | 6 | 13 | 10 | 11 |
| 4 | 26 | 5 | 10 | 6 | 21 | 17 |
| 5 | 13 | 16 | 16 | 7 | 20 | 8 |
| 6 | 31 | 5 | 20 | 2 | 25 | 10 |
Select a cluster sample of 3 clusters from the given data and find sample mean.
An experiment was planned to study the effect of Sulphate, Potash and Super Phosphate on the yield of potatoes. All the combinations of 2 levels of Super Phosphate [0 cen and 5 cent
acre] and two levels of Sulphate and Potash [0 cen
and 5 cent
acre] were studied in a randomised block design with 4 replications each. The (1/70) yields [lb per plot = (1/70) acre] obtained are given in table below:
| Blocks | Yields | |||
| I | (1) 23 | k 25 | p 22 | kp 38 |
| II | p 40 | (1) 26 | k 36 | kp 38 |
| III | (1) 29 | k 20` | pk 30 | p 20 |
| IV | kp 34 | k 31 | p 24 | (1) 28 |
Analyse the data and give your conclusions.
A sample of 100 villagers is to be drawn from a population of villages A and B. The population means and population mean squares of their monthly wages are given below:
| Village | |||
| Collage A | 400. | 60 | 20 |
| Collage B | 200 | 120 | 80 |
Find the number of samples using Proportional and Neyman allocation techniques and compare. Obtain the sample mean and variances for the Proportional Allocation and SRSWOR for the given information. Then Find the percentage gain in precision of variances of sample mean under the proportional allocation over that of SRSWOR.