# Statistical Methods-Tests of Significance (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 1 - 4 of 17

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## Question number: 1

» Statistical Methods » Tests of Significance » Chi-Square

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Appeared in Year: 2013

Essay Question▾

### Describe in Detail

From along series of annual river flows, the variance is found out to be 49 units. For a new sample of 25 years, the variance is calculated as 81 units. Can we regard that the sample variance is significant? (Given the chi-square value at 5 % level of significance as 37.7)

### Explanation

The sample size is 25. Here we test

The null hypothesis is tested by chi-square test when the sample size is less than 30. The test statistic is

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## Question number: 2

» Statistical Methods » Tests of Significance » T-Test

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Appeared in Year: 2014

Essay Question▾

### Describe in Detail

Define power of a test and discuss its role in selecting the best test. Describe a test procedure for testing equality of means of two independent normal populations, when standard deviations are equal but unknown for small samples.

### Explanation

Power of a test: The power function is the probability of rejection the null hypothesis when the alternative hypothesis is true. In statistical terms,

The quantity 1-β is called the power of the test. So, the power of the test is depends upon the difference between the parame

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## Question number: 3

» Statistical Methods » Tests of Significance » Z-Test

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Appeared in Year: 2009

Essay Question▾

### Describe in Detail

A manufacturer of alkaline batteries expects that only 5 % of his products are defective. A random sample of 300 batteries contained 10 defectives. Can we conclude the proportion of defectives in the entire lot is less than 0·5 at 5 % level of significance?

### Explanation

A random sample of 300 batteries contained 10 defectives. A manufacturer of alkaline batteries expects that only 5 % of his products are defective that is testing of hypothesis is

H 0: P = 0.05 against H 1: P < 0.05

Here n = 300, numbers of defectives is 10 and

The estimated value of P is

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## Question number: 4

» Statistical Methods » Tests of Significance » T-Test

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Appeared in Year: 2010

Essay Question▾

### Describe in Detail

You are working as a purchase manager for a company. The following information has been supplied to you by two manufacturers of electric bulbs.

 Company A Company B Mean life 1300 1288 Standard deviation 82 93 Sample size 100 100

Which brand of bulbs are you going to purchase if you desire to take a risk of 5%?

### Explanation

Here the sample size is n = 100

The standard deviation and mean of two samples is different. The null hypothesis is the mean life of bulb of company A is equal to the mean life of bulb of company B and alternative its differ.

The test statistic is

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