A company appointed four salesman A, B, C and D and observed their sales in three
seasons – Summer, Winter and Monsoon. Test whether the average sales of the four
salesmen differ in amount (in Rs. Lakhs) as given below by one-way analysis of
variance (ANOVA) using observations after taking deviation from 30.
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There are 1000 pages in a book out of which 100 pages are defective. What is the
probability that out of first 50 pages 10 pages will be defective?
Construct a continuous frequency distribution for the following heights (in cm) of 50
students in a class and draw its frequency polygon:
146 156 152 167 178 180 172 162 148
153 161 173 163 174 147 179 148 151
168 172 165 173 172 180 175 145 153
154 162 164 170 172 160 161 158 152
163 165 170 168 158 149 155 160 150
149 167 176 169 159
1000 students at college level were graded according to their IQ levels and the economic condition of their parents, as follow:
| Economic condition | IQ level | ||
| High | Low | Total | |
| Rich | 230 | 170 | 400 |
| Poor | 230 | 130 | 600 |
|
Total | 700 | 300 | 1000 |
A population of size 10000 is divided into 4 strata. Their sizes and standard
deviations are given below:
A stratified random sample of size 500 is to be drawn from this population.
Determine the sizes of samples from these strata, in case
i) Proportional allocation is used.
ii) Neyman’s optimum allocation is used.
A hospital has 25 centres located at different places in a state. Each centre has been provided with 4 paramedics. In order to estimate the average number of patients handled by a paramedic on a typical day at a centre, a sample of 5 centres was selected, using without replacement simple random sampling. The data regarding the number of patients on a typical working day for each selected centre are given below:
| Centre | m | Patients seen | |||
| 1 | 4 | 1 | 2 | 6 | 3 |
| 2 | 4 | 4 | 3 | 2 | 2 |
| 3 | 4 | 5 | 3 | 2 | 1 |
| 4 | 4 | 4 | 1 | 5 | 6 |
| 5 | 4 | 2 | 3 | 4 | 7 |
An insurance company insured 1000 scooter drivers, 3000 car drivers and 6000 truck
drivers. The probabilities that the scooter, car and truck drivers meet with an
accident, are 0.02, 0.04 and 0.25, respectively. One of the insured driver meets with
an accident. What is the probability that he is a (i) car driver; (ii) truck driver?
Two sets of ten students selected at random from a college were taken; one was given memory test as they were and the other set was given a memory test after two weeks’ training and the scores are given below:
| Set A | Set B |
| 10 | 12 |
| 8 | 8 |
| 7 | 8 |
| 9 | 10 |
| 8 | 8 |
| 10 | 11 |
| 9 | 9 |
| 6 | 8 |
| 7 | 9 |
| 8 | 9 |