ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 65 - 68 of 165

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Question number: 65

» Statistical Methods » Association and Contingency

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Appeared in Year: 2014

Essay Question▾

Describe in Detail

A medicine supposed to have effect in preventing TB was treated on 500 individuals and their records were compared with the records of 500 untreated individuals as follows. Study the effectiveness of medicine by calculating (i) Yule’s coefficient of association (ii) Yule’s coefficient of colligation.

-

No-TB

TB

Treated

252

248

Untreated

224

276

Explanation

The frequencies for various attributes be show in this contingency table

-

No-TB (A)

TB (a)

Treated (B)

(AB)

(aB)

Untreated (b)

(Ab)

(ab)

(i) Yule’s coefficient of association is a relative measure of association between two attributes, for this question the attributes are No-TB and treatment. If (AB

… (51 more words) …

Question number: 66

» Statistical Methods » Data » Multivariate

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Appeared in Year: 2011

Essay Question▾

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The following are the frequencies in the given intervals:

(0 - 2)

(2 - 5)

(5 - 10)

(10 - 15)

(15 - 18)

(18 - 20)

43

85

151

112

72

34

Draw the histogram of this data. Calculate the mean of the data from the frequency table.

Explanation

The histogram of the frequencies is given where the widths of all classes are not equal.

Class interval

mid value

Frequencies

(0 - 2)

1

43

(2 - 5)

3.5

85

(5 - 10)

7.5

151

(10 - 15)

12.5

112

(15 - 18)

16.5

72

(18 - 20)

19

34

Hence, the mean of t

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Question number: 67

» Statistical Methods » Tests of Significance » Z-Test

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Appeared in Year: 2014

Essay Question▾

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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

Let X follow a binomial distribution B (n, P) with mean nP and variance nP (1-P). In testing the hypothesis

H 0: P = P 0 against H 1: P > P 0

The null hypothesis can be tested by z-test for assuming the sample size n is large (Central limit theorem). For binomial distribution, the test statistic is

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Question number: 68

» Numerical Analysis » Inverse Interpolation

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Appeared in Year: 2015

Essay Question▾

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Compute the value of by Simpson’s 1/3 rd rule. Given that ln4.0 = 1.39, ln4.2 = 1.43, ln4.4 = 1.48, ln4.6 = 1.53, ln4.8 = 1.57, ln5.0 = 1.61, ln5.2 = 1.65

Explanation

So, the seven ordinates of the integrand using Simpson’s rule is

Where h = 1/6 (b-a) and y k =f (a + kh) for k = 0,1, 2,3, 4,5, 6

Here, b = 5.2, a = 4, h = 0.2, f (x) = lnx

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