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32.

_ Write any four merits and any three demerits of standard deviation.

‎Explain principle of least squares.‏ ۔

‎Find the size and power of the following test. Reject H_:2=1in favour of H, : A= 2 whenever
‏بلا‎ +X, 2 2. Assume that X. and ‏بلا‎ are independent observations from a Poisson distribution
with parameter A.

‎. Explain paired t test.

‎. Explain analysis of variance one way classification. (10 Marks)
State and prove Baye’s theorem. (10 Marks)
A random sample of size nis taken from a normal population with mean zero and variance तः.

‎1
‎Niet
‎find the variance of t. (10 Marks)

‎Examine whether t= ॐ is a minimum variance bound unbiased estimator of o*. Hence

‎(1) Explain stratified sampling and what are its merits ?

‎(2) Explain cluster sampling. (10 Marks)
For the rectangular distribution over the interval (೮, 6), where ‏ه‎ ಇ 0. Find the maximum
likelihood estimators for a and B. (10 Marks)
Obtain (1 - ०)100% confidence interval for the difference of means of two independent
normal populations N(jt,,0;) and (ய, 0), when ೮] and ठः are known (10 Marks)
Explain the t test for testing the equality of means of two normal populations. (10 Marks)

‎Explain Chi-square goodness of fit test. (10 Marks)

‎€ test concerning the mean of a normal population when population variance
(10 Marks)

‎(a) How can the ‏ا5‎ art control chart be prepared ?
(b) How to interpret Shewhart control chart ? (10 Marks)

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