The monthly income (in Rs. Lakhs) of five employees in a company are as follows:
25, 20, 30, 15, 10. (i) List all possible samples (without replacement) of size 2 (ii)
Compute the mean of all samples and set up the sampling distribution of sample
mean.
(i) To list all possible samples of size 2 without replacement from the given monthly income data of five employees, you can consider all the combinations of two employees. There are ten such combinations:
1. {25, 20}
2. {25, 30}
3. {25, 15}
4. {25, 10}
5. {20, 30}
6. {20, 15}
7. {20, 10}
8. {30, 15}
9. {30, 10}
10. {15, 10}
These are all the possible samples of size 2 that can be drawn from the dataset.
(ii) To compute the mean of all
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In a locality, 100 persons were randomly selected and asked about how far they had studied. The results are shown in table given below
|
| Middle School | High School | College |
| Male | 10 | 15 | 25 |
| Female | 25 | 10 | 15
|
In a partially destroyed laboratory record of an analysis of correlation data, the
following results are legible:
The equations of two regression lines are as follows:
3Y 9X 46
3X 12Y 19
 
 
Obtain (i) mean values of X and Y; (ii) the values of regression coefficients; and (iii)
the value of correlation coefficient.
State whether the following statements are true or false. Give brief justification.
a) The number of samples of size 3 with replacement from a population of size 6 is 20.
b) If the odds in favour of an event A are 3 : 4, then the probability of occurrence of A
will be 4/7.
c) If the level of significance is the same, the area of the rejection region in a 2-tailed
test is less than that in a 1-tailed test.
d) There is no seasonal variation in an annual time series.
e) In a binomial distribution, if X represents the number of successes in 25 trials and the
probability of success at each trial is 0.5, then the standard deviation of X is 2.
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.
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 |
A random sample of 170 boys from 8502 boys in an area showed that 21 had some
nutritional deficiency. Estimate the proportion of nutritionally deficient boys and the
standard error of the estimate. Find the confidence interval also.
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?