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:
x | 3 | 4 | 5 | 6 |
f (x) | -2.8 | -1.2 | -0.3 | 1.8 |
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
Patient | Before | After |
1 | 100·0 | 98·1 |
2 | 102·1 | 97·2 |
3 | 100·6 | 98·6 |
4 | 100·1 | 99·1 |
5 | 101·5 | 97·6 |
6 | 102 | 98·6 |
7 | 99·9 | 98·2 |
8 | 102·7 | 98·1 |
9 | 100.40 | 98·2 |
10 | 100·8 | 97.1 |
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
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
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
Appeared in Year: 2013
Describe in Detail
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
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. no | x | y | Xy | x 2 |
1 | 0 | 5.01 | 0 | 0 |
2 | 2 | 10 | 20 | 4 |
3 | 4 | 31.62 | 126.48 | 16 |
Sum | 6 | 46.63 | 146.48 | 20 |
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