LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

**B.Sc.** DEGREE EXAMINATION – **STATISTICS**

FIFTH SEMESTER – NOVEMBER 2012

# ST 5505/ST 5501 – TESTING OF HYPOTHESES

Date : 03/11/2012 Dept. No. Max. : 100 Marks

Time : 9:00 – 12:00

__PART – A__

**Answer ALL Questions: ( 10 x 2 = 20 Marks )**

- Distinguish between Simple and Composite hypotheses.
- Define Best Critical Region.
- Define Exponential Distribution.
- When do you call a test uniformly most powerful?
- Define SPRT for testing Ho against H
_{1}. - State the ASN function for the SPRT for testing H
_{o}: q = q_{0}against H_{1}: q = q_{1}. - What do you mean by one-tailed and two-tailed tests?
- State the assumptions for Student’s t-test.
- Mention the assumptions associated with Non-parametric tests.
- State the situations where Sign test can be applied.

__PART – B__

**Answer any FIVE questions: ( 5 x 8 = 40 Marks )**

- Explain the concept of critical region.

12 Define and elaborate two types of errors in testing of hypothesis.

- Discuss the general approach of likelihood ratio test.
- Find the LRT of H
_{o}: q = q_{0}against H_{1}: q ≠ q_{o}based on sample of size 1 from the density

f ( x, q ) = 2 ( q – x ) / q^{2} , 0 < x < q

- Explain the concepts
- i) Level of Significance
- ii) Null and Alternative hypotheses.
- A manufacturer of dry cells claimed that the life of their cells is 24.0 hours. A sample of

10 cells had mean life of 22.5 hours with a standard deviation of 3.0 hours. On the basis of

available information, test whether the claim of the manufacturer is correct.

17 In a breeding experiment, the ratio of off-spring in four classes was expected to be 1:3:3:9.

The experiment yielded the data as follows:

Classes AA Aa aA aa

No.of offsprings: 8 29 37 102

Test whether the given data is in agreement with the hypothetical ratio.

- Use the sign test to see if there is a difference between the number of days required to collect

an account receivable before and after a new collection policy. Use the 00.5 significance level

Before: 33 36 41 32 39 47 34 29 32 34 40 42 33 36 27

After : 35 29 38 34 37 47 36 32 30 34 41 38 37 35 28

__PART – C__

**Answer any TWO questions: (2 x 20 = 40 Marks )**

19 a) State and Prove Neymann-Pearson Lemma.

- b) A sample of size 1 is taken from density

f ( x, q ) = 2 ( q – x ) / q^{2} , 0 < x < q

= 0 else where

Find an Most Powerful test of H_{o}: q = q_{0} versus H_{1}: q = q_{1} ; q_{0} > q_{1 } at level α .

20 a) Describe the sequential procedure for testing H_{o}: q = q_{0} against H_{1}: q ≠ q_{1} where q is the

parameter of the Poisson distribution.

- b) The heights of ten children selected at random from a given locality had a mean 63.2 cms

and variance 6.25 cms. Test at 5 % level of significance the hypothesis that the children of

the given locality are on the average less than 65 cms in all. Given for 9 degrees of freedom

P( t.> 1.83) = 0.05.

- a) Explain Chi-square test of Goodness of fit.

- b) The following table gives the number of aircraft accidents that occurred during the seven

days of the week. Find whether the accidents are uniformly distributed over the week.

Days : Mon Tue Wed Thur Fri Sat Total

No.of accidents : 14 18 12 11 15 14 84

- a) Find 99 % confidence limits for the parameter l in Poisson distribution.

- b) Apply Median Test for the following data:

X: 27 31 32 33 34 29 35

Y: 28 30 30 24 25 26

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