By V. Rajagopalan

ISBN-10: 8122418406

ISBN-13: 9788122418408

ISBN-10: 8122424295

ISBN-13: 9788122424294

This e-book can assist them to interpret their information themselves in a greater demeanour. during this publication, often used statistical exams are offered in an easy and comprehensible means with genuine existence examples and workouts.

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**Extra info for Selected Statistical Tests**

**Example text**

Assumption The population from which, the sample drawn is normal distribution. Null Hypothesis H0: The population variance σ 2 is σ 20 . That is, there is no significant difference between the assumed population variance σ 20 and the sample variance s2. , H0: σ 2 = σ 20 . Alternative Hypotheses H1(1) : σ 2 ≠ σ 20 H1(2) : σ 2 > σ 20 H1(3) : σ 2 < σ 20 Parametric Tests 21 Level of Significance ( α ) and Critical Region (1) χ2 < χ21– (α/2),n ∪ χ2 > χ2(α/2), n such that P{χ2 < χ21– (α/2),n ∪ χ2 > χ2(α/2), n } = α α/2← 2 2 χ (α / 2 ), n χ1− (α / 2 ), n 0 { →α/2 } (2) χ 2 > χ2 α, n such that P χ2 > χ2 α, n = α →α 0 (3) χ2 < χ21–α, n such that P {χ2 < χ21–α, n} = α.

H1: σ 12 > σ 22. 54 13 Conclusion: Since F < F á,(n −1 ,n −1 ) , we conclude that the data do not provide us any evidence 1 2 against the null hypothesis H0, and hence it is accepted at 5% level of significance. That is, there is no significant difference in variability between assembly line A and assembly line B in the number of defects. Example 2 An insurance company is interested in the length of hospital-stays for various illnesses. The company has selected 15 patients from hospital A and 10 from hospital B who were treated for the same ailment.

A random sample of 125 TVS make gave a mileage of 90 km. A random sample of 150 two wheelers of all other brands gave a mileage of 80 km. It is known that the standard deviation of both TVS Company and all other brands was 12 km. If significance is 5%, do TVS vehicles give a better mileage? Solution Aim: To test the average mileage of TVS two-wheelers with that of other brands is equal or more. H0: The average mileage of TVS two-wheelers (µ1) and all other brands (µ2) are equal. , H0: µ1 = µ2. H1: The average mileage of TVS two-wheelers is more than that of all other brands.

### Selected Statistical Tests by V. Rajagopalan

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