One-way analysis of variance is a generalization of the two sample t-test.
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.
Assume that you have to perform a sample survey for Family expenditure of the faculty of Indira Gandhi National Open University. Then explain the main steps involved in the planning and execution of that sample survey.
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.
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.
In SRSWOR, the possible numbers of sample of size n from a population of size N if sampling is done with replacement is Nn .
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.
If strata are heterogeneous then stratified sampling schemes provides estimates with greater precision.