ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 157 - 161 of 165
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Question number: 157
» Statistical Methods » Tests of Significance » F-Test
Appeared in Year: 2014
Describe in Detail
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]
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.
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Question number: 158
» Statistical Methods » Non-Parametric Test » Mann-Whitney
Appeared in Year: 2009
Describe in Detail
Given the following data:
| x | 0 | 1 | 3 |
| f (x) | 1 | 3 | 55 |
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).
Explanation
Let the a polynomial is P (X) = kx 2 +lx + m, where k, l, m are constants which is determine by using Lagrange’s interpolation polynomial because the x values is not equal interval.
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Question number: 159
» Statistical Methods » Tests of Significance » Chi-Square
Appeared in Year: 2009
Describe in Detail
Explain the method of testing normality by using chi-squared test.
Explanation
Let X is a random variable follows normal distribution with mean µ and variance σ 2. The testing of null hypothesis is that the population variance σ 2 equals a specified value against one of the usual alternatives σ 2 < , σ 2 > , or σ 2 . The appropriate statistic on which to base our d
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Question number: 160
» Probability » Laws of Total and Compound Probability
Appeared in Year: 2011
Describe in Detail
Verify the following identities:
(i)
(ii)
Explanation
Let A and B are two possible events in the sample space.
(i) Additive law of probability is
{Commutative property }
We know that
T
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Question number: 161
» Numerical Analysis » Interpolation Formulae » Newton-Gregory
Appeared in Year: 2010
Describe in Detail
Estimate U 2 from the following table:
| x | 1 | 2 | 3 | 4 | 5 |
| U x | 7 | - | 13 | 21 | 37 |
Explanation
To find the missing value, we use binomial expansion method. Here 4 values are known, we would take fourth order finite difference zero. Thus,
Here for x = 1, U 0 =7, U 1 =? , U 2 =13, U 3 =21, U 4 =37
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