Kerala University 2005 B.C.A Computer Application Test of Hypothesis - Question Paper
****.................................................... (3 pages) K6017
Name................................................
FOURTH SEMESTER B.C.A. DEGREE EXAMINATION, APRIL/MAY 2005
Optional SubjectStatistics Paper VIIITESTING OF HYPOTHESIS
Time : Three Hours Maximum : 90 Marks
Each unit carries 50 marks,
Not more than 30 marks will be awarded from each unit.
Statistical tables will be provided on request.
1. Explain why there are two type of errors in a statistical hypothesis ? (4 marks)
2. Explain the terms :
(a) Size of a test.
(b) Level of significance,
(c) Power of the test.
(d) Most powerful test.
_ marks)
3. State and prove Neymann-Pearson lemma. (8 marks)
4. Let Xj, Xn be a random sample from a normal population with mean and variance. Find the most powerful size-a test for H0: n = 10 versus H,: n = 25.
(8 marks)
5. Let X, 2 be the critical region for testing H,,: 0 = 1 against the alternative Hj: 0 = 3 on the basis of a single observation Xj from the population.
[ 0 , elsewhere
Obtain the chances of type I and type II errors and power of the test.
(8 marks)
6. Let X,, Xj, . . ., be a random sample from a normal distribution with unknown mean p. and variance 4. Use likelihood ratio test to obtain the best critical region of size a, under H0: n = 0 against H : n > 0.
(8 marks)
7. Explain the advantages of parametric test over non-parametric tests. (4 marks)
8. Define power function and explain its use iin testing hypothesis. (4 marks)
Turn over
9. Explain the role of central limit theorem in large sample tests. (4 marks)
10. It is known that the survival rate from a certain disease for the entire population is 80 %. However, in a sample of 100 old partients only 72 survived. Will you accept the hypothesis that the survival rate of the elderly people is less than that of the entire population at 5 % level of significance ?
(7 marks)
11. Samples of workers Were drawn from two factories and from them wages/day in Rupees, means, and standard deviation are calculated. Make a large sample test to test the significance of the difference between the wages in the two factories :
|
Mean |
S.D. |
Size of the sample | |
|
Factory A |
122 |
42 |
200 |
|
Factory B |
128 |
50 |
350 |
(7 marks)
12. (a) Explain the testing procedure to test the significance of correlation coefficient.
(b) What do you mean by paird t-test ?
* (7 marks)
13. A certain baby food given to each of the 14 babies resulted in the following increase in body weights :
2 1.2 .-0.5 1.7 -1.1 0.5 - 0.7 1.8 0.9 -0.7 2.2 -1.2 1.4 -0.4 Can it be concluded that use of the baby food increase the weights of babies ?
(8 marks)
14. Explain the F-test to test the equality of population variances. State the assumptions clearly.
(5 marks)
15. Dibcuss the x2-test of goodness of fit of a theoretical distribution to an observed frequency distribution.
(5 marks)
16. 1025 college students were classified according to their intelligence and economic conditions. Test whether economic condition and intelligence of the students are independent:
Intelligence Excellent Good Not good Good 55 190 252
Economic conditions
17. Let X,, ----, Xnbe a random sample from the p.d.f. f(x) ~ j
of Y= max. (X,, X,,..X) and Z = min. (X,, X*).
0 < x < 1 elsewhere
. Derive the p.d.f s
18. Explain the main advantages of non-parametric tests.
(8 marks) (4 marks) (6 marks) (6 marks)
19. What do you mean by a run ? Explain Wald-Wolfowitz run test.
20. Derive the sign test, stating dearly the assumptions made.
21- The Win-Lose record of a cricket team for the last 30 consecutive games was as follows :
WWLLLLWWLWLLWWWLWLWWLWLLLWWLWW Apply run test to test the sequence of wins (W) and loses (L) are random.
(6 marks)
22- Explain Mann-Whitney-Wilconon test. Obtain the mean and variance of the test statistics.
* (7 marks)
23. Explain Kolmogorov-Smimov two sample test. (7 marks)
24. Describe the median test for two sample location problem. (6 marks)
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| Earning: Approval pending. |
