1
LOYOLA COLLEGE (AUTONOMOUS), CHENNAI 600 034
B.Sc.DEGREE EXAMINATION -STATISTICS
FOURTH SEMESTER APRIL 2018
16UST4MC01- TESTING OF HYPOTHESES
Date: 20-04-2018 Dept. No. Max. 100 Marks
Time: 09:00-12:00
Part A Answer ALL the Questions:
1. What is meant by Type-I error?
2. Define most powerful test.
3. Define two-tailed test with example.
4. Define standard error of a statistic.
5. Define the best critical region.
6. What is composite hypothesis
7. Mention any two uses of Chi-square test.
8. Obtain the number of runs in the sequence xxyyxxxyxxyyyxx.
9. Write any two disadvantages of non-parametric test.
10. Define sign test.
Part B Answer any FIVE questions:
11. Describe critical region and acceptance region.
12. A single observation is taken from θ 0 x ∞. To test H0: θ=2
againstH1:θ=1. Find the best critical region of size 0.05.
13. Show that the family θ 0 has MLR property.
14. Explain how you will test for the significance of difference between two samples
Proportions.
15. The scores of 10 candidate's performance before and after training are given below.
Using Sign test, verify whether the given training is effective
Before
84
48
36
37
54
69
83
96
90
65
After
90
58
56
49
62
81
84
86
84
75
16. Explain the concepts of SPRT
17. The increase in weight when children are given two different diets A and B in the
same period measured in pounds are
Diet A
8
5
7
8
3
2
7
6
5
7
Diet B
3
7
5
6
5
4
4
5
3
6
Test whether the diets are significantly different.
18. Explain the test for the significant for variance of normal distribution.
2
Part Answer any two questions
19. State and prove Neymann Pearson lemma
20. Obtain the most powerful test of size α for testing H0:σ σ0 VS H1:σ σ1 in
Eplain
uniformly most powerful test
Likelihood ratio test
21. Derive the LRT for testing the equality of means of two independent Normal
populationswith equal variance.
22. Explain median test for the two samples.
Explain Mann Whitney U-test.