If experimental error is reduced considerably and the efficiency of the design is decreased.
One-way analysis of variance is a generalization of the two sample t-test.
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 |
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 .
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.
A manufacturer wishes to determine the effectiveness of four types of machines (A, B, C and D) in the production of bolts. To accumulate this, the numbers of defective bolts produced for each of two shifts in the results are shown in the following table:
| Machine | First Shift | Second Shift | ||||||||
| A | 6 | 4 | 5 | 5 | 4 | 5 | 7 | 4 | 6 | 8 |
| B | 10 | 8 | 7 | 7 | 9 | 7 | 9 | 12 | 8 | 8 |
| C | 7 | 5 | 6 | 5 | 9 | 9 | 7 | 5 | 4 | 6 |
| D | 8 | 4 | 6 | 5 | 5 | 5 | 7 | 9 | 7 | 10 |
Perform an analysis of variance to determine at 5% level of significance, whether there is a difference (a) Between the machines and (b) Between the shifts.
A manufacturer wishes to determine the effectiveness of four types of machines (A, B, C and D) in the production of bolts. To accumulate this, the numbers of defective bolts produced for each of two shifts in the results are shown in the following table:
| Machine | First shift | Second Shif | ||||||||
| M | T | W | Th | F | M | T | W | Th | F | |
| A | 6 | 4 | 5 | 5 | 4 | 5 | 7 | 4 | 6 | 8 |
| B | 10 | 8 | 7 | 7 | 9 | 7 | 9 | 12 | 8 | 8 |
| C | 7 | 5 | 6 | 5 | 9 | 9 | 7 | 5 | 4 | 6 |
| D | 8 | 4 | 6 | 5 | 5 | 5 | 7 | 9 | 7 | 10 |
Perform an analysis of variance to determine at 5% level of significance, whether there is a difference (a) Between the machines and (b) Between the shifts.