1. Write any two merits and demerits of Arithmetic Mean. Given below is the data about the number of seeds in a pod of a certain plant. Find the variance:

No. of Seeds 1 2 3 4 5 6
Frequency 8 14 7 12 3 1

2. Division A and B in a school have 20 students each. One student is to be selected from each division. What is the probability that Rahul in division A will be selected, if 2 students are selected out of 40 students?

3. A die is rolled 1200 times with the following results:

No. that comes up 1 2 3 4 5 6
Frequency: 195 289 202 242 163 109

Test, if the die is unbiased at level of significance. (Given that X^2 0.05(5) 11.07)

4. Define simple random sampling. Describe the limitations of simple random sampling. Differentiate SRSWR and SRSWOR methods of simple random sampling.

5. Cancer is present in 22% of a population and is not present in the remaining 78%. An imperfect clinical test successfully detects the disease and with probability 0.70. Thus, if a person has the disease in the serious form, the probability is 0.70 that the test will be positive and it is 0.30 if the test is negative. Moreover among the unaffected persons, the probability that the test will be positive is 0.05. A person selected at random from the population is given the test and the result is positive. What is the probability that this person has the cancer? 5

6. The probability that Meena is on time to catch the bus to her office is 0.8. Find the probability that she is late

exactly twice in a 6-day week, and

at least once in a 6-day week.

7. In a partially destroyed laboratory, record of an analysis of correlation of data, only the following results are legible

Variance of x 9. Regression equations

8x 10y 66 0

40x 18y 214 0

What were

the means of x and

the coefficient of correlation between x and

the standard deviation of

8. The following table shows the sample values of 3 independent normal random variables, X1, X2 and X3. Assuming that they have equal variances, test the hypothesis that they have the same mean by using ANOVA (Given =4.26)

X1 13 11 16 22
X2 16 08 21 11
X3 15 12 25 10

9. The following table gives, for a sample of married women, the level of education and marriage adjustment score

<img src='./qimages/13114-9.jpg'>

Can you conclude from the above, the higher the level of education, the greater is the degree of adjustment in marriage?
Given X^2 0.05) =9.488.

10. A population of size 500 is divided into 4 strata. The following table gives the data on size and standard deviation of each stratum

<img src='./qimages/13114-10.jpg'>

A stratified random sample of size 100 is to be drawn from the population. Determine the size of samples from each of these strata for:

Proportional Allocation,

Neyman's optimum allocation.