1. Calculate the mean and standard deviation for the following data <img src='./qimages/8433-1.jpg'> <br><br>

2. Find the correlation coefficient between two variables X and Y and the slope of regression line Y on X i.e.,byx The observations on 20 pairs are as follows <img src='./qimages/8433-2.jpg'> <br><br>

3. Box X contains 5 red and 4 blue balls, Box Y contains 2 red and 5 blue balls. A ball is drawn at random from each box. Find the probability of drawing one red and one blue ball. 5

4. Suppose of the items made in a factory are defective. Find the probability that there are 3 defective items in a sample of 100, and no defective item in a sample of 50.

5. Define time series and describe its components briefly, with examples.

6. Describe the following tests (in detail) Chi-square test for Goodness of fit
F-test for Equality of two variances

7. Differentiate between any two of the following:
Neyman Allocation and Optimum Allocation
Correlation and Regression
Random Sampling and Non-Random Sampling

8. The sales figures of a company are given below. Compute the moving averages for the length of 4 and 2 separately. <img src='./qimages/8433-8.jpg'> <br><br>

9. A dice is rolled 1200 times with the following results:

<img src='./qimages/8433-9.jpg'>

Test if the dice is unbiased at level of significance.