ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 157 - 162 of 165

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Explain the procedure for testing the hypothesis of equality of variances of two independent normal populations when population means are unknown. Write down the sampling distribution of the statistic. A sample of size 10 is drawn from each of two uncorrelated normal populations. Sample means and variances are:

1 ^st population: mean = 7, variance = 26

2 ^nd population: mean = 4; variance = 10

Test at 5 % level of significance whether the first population has greater standard deviation than that of the second population. [Given F _{0.05, 9, 9} = 3·18]

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Given the following data:

find a polynomial P (x) of degree 2 or less so that P (x) = f (x) at the tabulated values of x. Hence

approximate f (2).

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Explain the method of testing normality by using chi-squared test.

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Verify the following identities:

(i)

(ii)

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Estimate U ₂ from the following table:

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Show that is a probability density function for an appropriate value of a. Upto what order do the moments of this p. d. f. exist?