2. The branch of Statistics that deals with procedures and methodology for obtaining valid conclusions is called: (A) Descriptive (B) Advance (C) Inferential (D) All of these
3. Sum of the absolute deviations is least when deviations are taken from: (A) Mean (B) Median (C) Mode (D) Geometric Mean
4. In t-distribution, which one is true? (A) Mean = Median = Mode (B) Mean > Median > Mode (C) Mean < Median < Mode (D) All of these
5. What is the probability of a sure event? (A) 1 (B) 0 (C) 0.5 (D) 0.2
6. Which formula represents the probability of the complement of event A? (A) 1 + P(A) (B) 1 – P(A) (C) P(A) (D) P(A) – 1
7. In regression analysis, the variable that is being predicted is: (A) Dependent variable (B) Independent variable (C) Intervening variable (D) None of these
8. Paired t-test is applicable when the observations in the two samples are: (A) Equal in number (B) Paired (C) Correlated (D) All of these
9. The degree to which numerical data tend to spread about an average is called: (A) Dispersion (B) Regression (C) Correlation (D) None of these
10. The types of estimates are: (A) Point estimate (B) Interval estimates (C) Estimation of confidence region (D) All of these
11. Ranking scale also includes the properties of ________ scale. (A) Nominal (B) Interval (C) Ratio (D) All of these
12. The difference between a statistic and the parameter is called: (A) Sampling error (B) Random error (C) Non-random error (D) Probability
13. The standard deviation of any sampling distribution is called: (A) Standard error (B) Non-sampling error (C) Type-I error (D) Type-II error
14. A survey conducted by a sampling design is called: (A) Sample survey (B) Population survey (C) Systematic survey (D) None of these
15. The sum of the frequencies of the frequency distribution of a statistic is equal to: (A) Sample size (B) Population size (C) Possible samples (D) Sum of X values
16. Sampling error can be reduced by: (A) Non-probability sampling (B) Increasing the population (C) Decreasing the sample size (D) Increasing the sample size
17. The range of test statistic t is: (A) 0 to ∞ (B) 0 to 1 (C) -∞ to +∞ (D) -1 to +1
18. The probability associated with committing a Type-I error is: (A) β (B) α (C) 1 – β (D) 1 – α
19. The degree of freedom for paired t-test based on n pairs of observations is: (A) 2n – 1 (B) n – 2 (C) 2(n – 1) (D) n – 1
20. Experimental error is due to: (A) Experimenter’s mistakes (B) Extraneous factors (C) Variation in treatment effects (D) None of these
PART – II(Subjective) 80 Marks
Attempt FOUR questions from PART-II by selecting TWO Questions from EACH SECTION.(20×4)
SECTION – A
Q. No. 2. (a) What is the purpose of frequency distribution and what are its desirable qualities? For a certain frequency distribution, the mean was 40.5 and the median 36. Find the mode approximately using the empirical formula connecting the three. (10)
(b) Define Statistics. Discuss the importance of the study of statistics by giving examples. How can it help the extension of scientific knowledge? (10)
Q. No. 3. (a) Explain what is meant by the skewness of the distribution, and define a suitable measure of Skewness. For a given p.d.f: f(x) = k(x – x²), for 0 ≤ x ≤ 1 and zero elsewhere. Find the Skewness and discuss the result. (10)
(b) Define the normal distribution and obtain its mean and variance. Show that for the normal distribution, the mean, mode and median are the same. (10)
Q. No. 4. (a) If X has a binomial distribution, then show that E(X) = np and Var(X) = npq. Derive the m.g.f of the binomial distribution and explain its uses. (10)
(b) What are the main characteristics of the Poisson distribution? Explain with the help of examples. Also give its properties, applications and relationship with other distributions. (10)
Q. No. 5. (a) From the following set of values: (10) Y: | 6.5 | 5.3 | 8.6 | 1.2 | 4.2 | 2.9 | 1.1 | 3.0 | X: | 3.2 | 2.7 | 4.5 | 1.0 | 2.0 | 1.7 | 0.6 | 1.9 |
(1) Compute the residuals and verify that they add up to zero, then draw a conclusion about the results. (2) Compute the standard error of estimate, S_(y.x).
(b) Under what conditions does the correlation among random variables exist? Also describe the properties of the correlation coefficient. Calculate the correlation coefficient for a sample of 20 pairs of observations, given that: (10) n = 20, Mean of X = 2, Mean of Y = 8, ΣX² = 180, ΣY² = 1424, ΣXY = 404 Also interpret the results.
SECTION – B
Q. No. 6. (a) What is the finite population correction (fpc) factor? When is it appropriately used in sampling applications and when can it, without great undesirable consequences, be ignored? (10)
(b) Given the population: 2, 4, 8, 8, 10, 10. (10) (1) How many samples of size n = 2 can be drawn without replacement from this population? (2) Compute and tabulate the sampling distribution of the mean for samples of size n = 2.
Q. No. 7. (a) Explain what is meant by: (10) (i) A statistical hypothesis (ii) Test-statistic (iii) Test of significance (iv) Level of significance (v) Type-I error and Type-II error
(b) The weights of 4 persons before they stopped smoking and 5 weeks after they stopped smoking are as follows: (10)
Person
1
2
3
4
Before
148
176
153
116
After
154
176
151
121
Use the t-test for paired observations to test the hypothesis at the 0.05 level of significance, that giving up smoking has no effect on a person’s weight.
Q. No. 8. (a) Explain the procedure of randomization in a completely randomized design (CRD) where we have 3 varieties of wheat and 18 experimental plots available. Also explain what is indicated by a significant F-value in an experiment. (10)
(b) Four varieties of wheat were tried in a randomized complete block design (RCBD) in four replications. Yield in kilograms per plot is shown in the table given below. Test the hypothesis that there is no difference in the means of the four varieties (Use α = 0.05). (10)
