ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 128 - 134 of 164

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Question 128

Appeared in Year: 2012

Describe in Detail

Essay▾

Solve the equation f (x) = 0 by using a suitable interpolation formula on the following values:

x3456
f (x)-2.8-1.2-0.31.8

Explanation

To solve the equation f (x) = 0, using Lagrange՚s inverse interpolation method

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Question 129

Appeared in Year: 2015

Describe in Detail

Essay▾

Prove that for r = 1,2, … , n

Explanation

We known that the L. H. S. is an incomplete gamma function and R. H. S. is a cumulative density function of Poisson distribution.

The incomplete gamma function is

Then

provided that r is an integer. Thus recall that Γ (r) = (r − 1) ! for r integer.

Rewriting this expression we arrive at the desired expression

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Question 130

Appeared in Year: 2011

Describe in Detail

Essay▾

Let the temperature before and after administration of aspirin be

PatientBeforeAfter
1100·098·1
2102·197·2
3100·698·6
4100·199·1
5101·597·6
610298·6
799·998·2
8102·798·1
9100.4098·2
10100·897.1

Test by the sign test; whether aspirin is effective in reducing temperature. What is the p-value of the calculated statistic?

Explanation

Let M1 and M2 is the median temperature of the patients. The hypothesis for test is

Fir this first find the difference of median

Also find the difference of temperature of before and after

di 2.1 4.9 2.0 1.0 3.9 3.4 1.7 4.6 2.4 3.7

Then find the sign of difference between di and d0 .

-+ -- ++ -+ -+

The number of positive sign is r = 5 and negative sign i…

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Question 131

Bivariate Normal Distribution
Edit

Appeared in Year: 2010

Describe in Detail

Essay▾

Show that for discrete distribution β2 > 1

Explanation

We have to prove that

By definition of Kurtosis

Let x1 , x2 , … , xn are n observations in a set have frequency f1 , f2, … , fn and the mean of observation is , then

Assume

which is always true because this a variance which is always positive

So, ‎

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Question 132

Edit

Appeared in Year: 2010

Describe in Detail

Essay▾

How large a sample must be taken in order that the probability will be at least 0·95 that Xn will be within 0·5 of µ (µ is unknown and σ = l) .

Explanation

Here, you would know the standard deviation of a population but not know the mean of that population. So, you want to estimate the mean μ to within a given margin of error in a given confidence interval. The required sample size is

Margin of error E = 0.5,

1-α = 0.95 ⇾ α = 0.05

σ = 1 and zα/2 = 1.96

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Question 133

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Appeared in Year: 2013

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Essay▾

Find the weighted arithmetic mean of the first ‘n’ natural numbers, the weights being the corresponding numbers.

Explanation

If x1 , x2 , … , xn are the values having weights w1 , w2 , … , wn respectively, the weight mean is

Here X is first ‘n’ natural numbers that is 1,2, 3, … , n

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Question 134

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Appeared in Year: 2015

Describe in Detail

Essay▾

Fit the exponential curve y = a + bx to the following data

x: 0 2 4

y: 5.01 10 31.62

Explanation

his is not exponential equation, it is a straight line y = a + bx

S. noxyXyx 2
105.0100
2210204
3431.62126.4816
Sum646.63146.4820

The normal equations is

Using the table , putting these values in normal equations. We get

Solving these two equations, we get the value of a and b

So, required line is y = 2.188 + 6.677x