Four groups of students were subjected to different teaching techniques and tested at the end of a specified period of time. As a result of dropouts from the experimental groups the number of students varied from group to group. Do the data shown below present sufficient
evidence to indicate a difference in the mean achievement for the four teaching techniques at 0.01 level of significance? What is the conclusion if you fix the level of significance at 0.05?
| Group 1 | Group 2 | Group 3 | Group 4 |
| 65 | 75 | 59 | 94 |
| 87 | 69 | 78 | 89 |
| 73 | 83 | 67 | 80 |
| 79 | 81 | 62 | 88 |
| 81 | 72 | 83 |
|
| 69 | 79 | 76 |
|
|
| 90 |
|
|
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A farmer has 200 metres of fencing with which he wishes to enclose a rectangular field. One side of the field can make use of a fence that already exists. What is the maximum area he can enclose?
Find the equation of the plane passing through (2,3, −1) and perpendicular to the line joining the points (3, 4, −1) and (2, −1, 5) .
Suppose that the temperature is normally distributed with expectation 50o C and variance 4o C . What is the probability that the temperature T will be between 48o C and 53o C ?
What is the probability that T ≥ 52o C ?
The probability that a person over 60 years of age in a certain community drinks alcohol 2/5 is
and the probability that a person over 60 years of age has heart disease is 2/15 . The
probability that a person over 60 years of age drinks alcohol and has heart disease is 1/16 . Are
‘drinking alcohol’ and ‘heart disease’ independent events?
Evaluate the following integrals:
i) 
ii) ∫ x ln | x + 1| dx
Four groups of students were subjected to different teaching techniques and tested at the end of a specified period of time. As a result of dropouts from the experimental groups the number of students varied from group to group. Do the data shown below present sufficient
evidence to indicate a difference in the mean achievement for the four teaching techniques at 0.01 level of significance? What is the conclusion if you fix the level of significance at 0.05?
| Group 1 | Group 2 | Group 3 | Group 4 |
| 65 | 75 | 59 | 94 |
| 87 | 69 | 78 | 89 |
| 73 | 83 | 67 | 80 |
| 79 | 81 | 62 | 88 |
| 81 | 72 | 83 |
|
| 69 | 79 | 76 |
|
|
| 90 |
|
|
An economist wants to estimate the relationship between a family’s annual income and the amount that the family saves. The family data for nine families are obtained
| Annual income (thousands of Rs.) | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| Annual saving (thousands of Rs.) | 0.0 | 0.1 | 0.2 | 0.2 | 0.5 | 0.5 | 0.6 | 0.7 | 0.8 |