ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 133 - 138 of 165
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Question number: 133
» Statistical Methods » Tests of Significance » Z-Test
Appeared in Year: 2010
Describe in Detail
How large a sample must be taken in order that the probability will be at least 0.95 that X n 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… (11 more words) …
Question number: 134
» Statistical Methods » Measures of Location
Appeared in Year: 2013
Describe in Detail
Find the weighted arithmetic mean of the first ‘n’ natural numbers, the weights being the corresponding numbers.
Explanation
If x 1, x 2, …, x n are the values having weights w 1, w 2, …, w n respectively, the weight mean is
Here X is first ‘n’ natural numbers that is 1, 2, 3, …, n
Question number: 135
» Numerical Analysis » Interpolation Formulae » Lagrange
Appeared in Year: 2015
Describe in Detail
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… (33 more words) …
Question number: 136
» Probability » Standard Probability Distributions » Uniform
Appeared in Year: 2011
Describe in Detail
Let X have the continuous c. d. f. F (x). Define U = F (x). Show that both - log U arid -log (1 - U) are exponential random variables:
Explanation
Let U = F (x), then the distribution function of G of U is given by
Since F is non-increasing and its continuous.
G (u) =F (F -1 (u) ) implies G (u) =u
Then the p. d. f is
Since F is a distribution function takes value… (54 more words) …
Question number: 137
» Statistical Methods » Tests of Significance » T-Test
Appeared in Year: 2015
Describe in Detail
Let X 1, X 2, …, X 12 be a random sample from a normal N (µ 1, σ 12) and Y 1, Y 2, …Y 10 be another random sample from normal N (µ 2, σ 22), independently to each other. Carry out an appropriate test for testing
at 5 % level of significance. It is given that .
Explanation
Let X 1, X 2, …, X 12 be a random sample from a normal N (µ 1, σ 12) and Y 1, Y 2, …Y 10 be another random sample from normal N (µ 2, σ 22), independently to… (87 more words) …
Question number: 138
» Probability » Conditional Probability
Appeared in Year: 2012
Describe in Detail
You arc given the following information:
(i) In random testing, you test positive for a disease.
(ii) In 5 % of cases, the test shows positive even when the subject does not have the disease.
(iii) In the population at large, one person in 1000 has the disease. What is the conditional probability that you have the disease given that you have been tested positive, assuming that if someone has the disease, he will test positive with probability 1?
Explanation
Let X denotes the test is positive and Y denotes the person has disease. Given that 5 % of cases, the test shows positive even when the subject does not have the disease that is
where denotes the person has no disease. Also given the test positive with… (41 more words) …