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1. ANOVA (Analysis of Variance) is primarily used to test the equality of which parameter across three or more groups?

2. A finite population has N = 400 observations and population standard deviation sigma = 3,000. A simple random sample of n = 80 is drawn without replacement. What is the standard error of the sample mean, using the finite population correction?

3. Consider the statements about the Coefficient of Variation (CV):
1. CV = (standard deviation / mean) x 100.
2. CV is an absolute measure of dispersion.
3. CV is useful for comparing variability across two or more series.
Which option is correct?

4. Standard deviation is the ______ root of ______.

5. Assertion (A): A normal distribution has a bell-shaped curve.
Reason (R): In a normal distribution, mean = median = mode.
Choose the correct relationship.

6. Given sigma_x = 4, sigma_y = 5 and regression coefficient b_yx = 0.8, find the correlation coefficient r using r = b_yx x (sigma_x / sigma_y).

7. The empirical relationship among mode, median and mean is: Mode = ______ Median – ______ Mean.

8. For a grouped distribution, modal class lower limit l = 20, f1 = 15, f0 = 10, f2 = 8 and class width h = 5. Using Mode = l + [(f1-f0)/(2f1-f0-f2)] x h, find the mode.

9. If mean = 100 and standard deviation = 20, what is the coefficient of variation?

10. Assertion (A): Time-series analysis commonly recognises four components – secular trend, seasonal variation, cyclical variation and irregular variation.

Reason (R): Time-series analysis is used only for short-term forecasting.
Choose the correct option.

11. Which statement correctly defines a Type I error in hypothesis testing?

12. Assertion (A): A Type I error occurs when a true null hypothesis is rejected.
Reason (R): The probability of a Type I error is denoted by alpha and the error is often called a false positive.
Which option is most appropriate?

13. The mean of the following grouped distribution is 54. Find the missing frequency x.
Class intervals: 0-20, 20-40, 40-60, 60-80, 80-100
Frequencies: 7, x, 10, 9, 13

14. How should these variables be classified statistically: building colour; percentage marks; number of defaults; executive body weights?

15. Which statements about the standard error (SE) of the mean are true?
1. It measures variability of sample means around the population mean.
2. It decreases as sample size increases, other things equal.
3. For n > 1, SE is smaller than the corresponding SD.
4. For simple random sampling from a very large population, SE = SD/sqrt(n).

16. Consider the following statements about the development and use of statistics:
1. The term Statistik is commonly associated with German scholar Gottfried Achenwall in the eighteenth century.
2. Achenwall used the term in 1749 in connection with the study of the state.
3. Modern statistical methods are confined only to physical and natural sciences.
Which option is correct?

17. Regarding the inclusive method of classifying a frequency distribution:
1. Both lower and upper class limits belong to the same class.
2. A value equal to the upper limit is always placed in the next class.
3. It is generally suited to discrete data expressed in whole units.
Which option is correct?

18. The modal class is 105-120 in the distribution below. If the mode is 115, find the missing frequency x.
Class intervals: 60-75, 75-90, 90-105, 105-120, 120-135
Frequencies: 30, 30, 60, x, 70

19. For a sample, sum(x-xbar)^2 = 1500, sum(y-ybar)^2 = 800 and sum[(x-xbar)(y-ybar)] = 1000. Find the Pearson correlation coefficient.

20. The mode and mean of a moderately skewed distribution are 36 and 30 respectively. Using the empirical relationship, find the median.

21. If the coefficient of correlation between two variables is +0.95, what does it indicate?

22. Which option correctly defines quartiles?

23. A firm maximises Z = 5X + 4Y subject to 2X + Y <= 14 and X + 2Y <= 14. Using a standard simplex tableau with the Cj-Zj convention, which variable enters the basis first?

24. A bakery buys each loaf for Rs. 25 and sells it for Rs. 35. It orders 100 loaves, demand is 90 loaves, and unsold bread has no salvage value. What is the profit?

25. A shop orders 80 units. Demand is 95 units. Selling price is Rs. 50 per unit and cost price is Rs. 40 per unit. What is the profit, assuming no other costs?

26. Daily demand over the last 10 days was 100, 110, 120, 130, 90, 100, 140, 120, 110 and 80 units. If the simple new ordering rule uses average demand, what quantity should be ordered?

27. In a simulation model, random numbers are mainly used to do what?

28. A bank identifies high-potential employees, creates a talent pool and gives them accelerated career paths, cross-functional exposure, leadership training and mentoring. Which HRD subsystem does this primarily represent?

29. A large bank has fragmented manual employee records, duplicated updates, inconsistent data and delayed statutory reports. Which solution is the most comprehensive?

30. What is the key feature of a 360-degree performance appraisal?