# Statistical Methods-Tests of Significance [ISS (Statistical Services) 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

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Appeared in Year: 2010

Essay Question▾

### Describe in Detail

For 2X2 table

 A b C d

prove that Chi-square test of independence gives

### 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 attributes A

Since the marginal frequencies is fixed, therefore

Probability for a individual belong to class A

Probability for a individual belong to class B

Since the cla

… (420 more words) …

## Question number: 6

» Statistical Methods » Tests of Significance » Z-Test

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Appeared in Year: 2014

Essay Question▾

### Describe in Detail

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 large (Central limit theorem). For binomial distribution, the test statistic is

… (211 more words) …

## Question number: 7

» Statistical Methods » Tests of Significance » Z-Test

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Appeared in Year: 2015

Essay Question▾

### Describe in Detail

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 . Suppose the samples of sizes n 1 and n 2 are selected from binomial populations are independent.

For large sample size, the estimator was approximat

… (122 more words) …

## Question number: 8

» Statistical Methods » Tests of Significance » F-Test

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Appeared in Year: 2012

Essay Question▾

### Describe in Detail

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 with different sample size n 1, n 2, …, n k. The test of null hypothesis is that the means of k normal population is same and the alternative hypothesis is any two mean are not same.

Vs H 1: at least two mean are no

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## Question number: 9

» Statistical Methods » Tests of Significance » F-Test

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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 1 2) and N (µ 2, σ 2 2) 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 1 2) and N (µ 2, σ 2 2).

In this question the hypothesis for testing is

Let s 1 2 and s 2 2 be the estimates variances of σ 1 2 and σ 2 2 based on sample sizes n and m.

and

… (379 more words) …

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