# 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

Appeared in Year: 2010

### Describe in Detail

For 2X2 table

A | b |

C | d |

prove that Chi-square test of independence gives

### Explanation

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## Question number: 6

» Statistical Methods » Tests of Significance » Z-Test

Appeared in Year: 2014

### 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

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## Question number: 7

» Statistical Methods » Tests of Significance » Z-Test

Appeared in Year: 2015

### 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

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## Question number: 8

» Statistical Methods » Tests of Significance » F-Test

Appeared in Year: 2012

### 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

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## Question number: 9

» Statistical Methods » Tests of Significance » F-Test

Appeared in Year: 2013

### 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

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