Statistical Methods-Tests of Significance (ISS Statistics Paper I (Old Subjective Pattern)): Questions 5 - 9 of 17

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Question number: 5

» Statistical Methods » Tests of Significance » Chi-Square

Appeared in Year: 2010

Essay Question▾

Describe in Detail

For 2X2 table

A

b

C

d

prove that Chi-square test of independence gives

χ2=N(adbc)(a+c)(b+d)(a+b)(c+d),N=a+b+c+d

Explanation

Let the contingent table is

Class

A

α

Total

B

a

b

a + b

β

c

d

c + d

Total

a + c

b + d

a + b + c + d =N

Here A denotes the presence of any attributes and α denotes the absence of… (453 more words) …

Question number: 6

» Statistical Methods » Tests of Significance » Z-Test

Appeared in Year: 2014

Essay Question▾

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Let X follow a binomial distribution B (n, P). Explain the test procedure for

H 0: P = P 0 against H 1: P > P 0

when the sample size is (i) small, and (ii) large. It is desired to use sample proportion p as an estimator of the population proportion P, with probability 0.95 or higher, that p is within 0.05 of P. How large should sample size (n) be?

Explanation

Let X follow a binomial distribution B (n, P) with mean nP and variance nP (1-P). In testing the hypothesis

H 0: P = P 0 against H 1: P > P 0

The null hypothesis can be tested by z-test for assuming the sample size n is… (228 more words) …

Question number: 7

» Statistical Methods » Tests of Significance » Z-Test

Appeared in Year: 2015

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If X follows binomial b (n 1, p 1) distribution and Y follows binomial b (n 2, p 2), provide an appropriate test at level α for H 0: p 1 =p 2 against H 1: p 1 > p 2.

Explanation

The hypothesis is equivalent to testing the null hypothesis that p 1 −p 2 = 0 against the alternative is p 1 -p 2 > 0. The statistic on which we base our decision is the random variable P^1P^2. Suppose the samples of… (142 more words) …

Question number: 8

» Statistical Methods » Tests of Significance » F-Test

Appeared in Year: 2012

Essay Question▾

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Indicate how you would test the hypothesis that the means of k independent normal populations are identical, clearly mentioning the null and the alternative hypotheses, the assumptions made, the test statistic used, and the critical region.

Explanation

Let there are k independent normal population N(μ1,σ12),N(μ2,σ22),,N(μk,σk2) with different sample size n 1, n 2, …, n… (311 more words) …

Question number: 9

» Statistical Methods » Tests of Significance » F-Test

Appeared in Year: 2013

Essay Question▾

Describe in Detail

Obtain 100 (1 -α) % confidence interval for the ratio of population variances by using two independent random samples from N (µ 1, σ 12) and N (µ 2, σ 22) under the assumption that the population means are (i) known and (ii) unknown.

Explanation

Let X 1, X 2, …, X n and Y 1, Y 2, …Y m are the samples taken from independent N (µ 1, σ 12) and N (µ 2, σ 22).

In this question the hypothesis for testing is… (451 more words) …

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