ISS (Statistical Services) Statistics Paper II (Old Subjective Pattern): Questions 8 - 12 of 39

Access detailed explanations (illustrated with images and videos) to 39 questions. Access all new questions we will add tracking exam-pattern and syllabus changes. Subscription can be renewed yearly absolutely FREE! View Sample Explanation or View Features.

Rs. 200.00 or

How to register?

Question number: 8

» Hypotheses Testing » Hypothesis » Composite

Edit

Appeared in Year: 2014

Essay Question▾

Describe in Detail

A sample of size n from normal distribution N (θ, σ 2 ) with σ 2 =4 was observed. 95 % confidence interval for θ was computed from the above sample. Find the value of n if the confidence interval is (9.02,10.98).

Explanation

The Margin of error is defined as

Where z α/2 is the critical value = 1.96

σ is the standard deviation = 2

E is the margin of error=

… (88 more words) …

Question number: 9

» Hypotheses Testing » Randomised Test

Edit

Appeared in Year: 2014

Essay Question▾

Describe in Detail

Bring out the difference between a randomized and non-randomized test. Explain how the decision based on a randomized test can be taken in the discrete set-up.

Explanation

A test T of a hypothesis H is said to be non-randomized test if the decision about the rejection or acceptance of H is based on a test statistic. H is rejected if the test statistic lies in the critical region otherwise accepted. A randomized test is one in which no test statistics is involved. The decision about H is taken on the basis of some p

… (61 more words) …

Question number: 10

» Linear Models » Analysis of One-Way Classified Data » Mixed Model

Edit

Appeared in Year: 2014

Essay Question▾

Describe in Detail

A manufacturer of television sets is interested in the effect on tube conductivity of five different types of coating for color picture tubes. Sample means are

Error sum of squares = 54.0

(i) Is there a difference in conductivity due to coating type? F-value = 3.09

(ii) Determine which pair differs significantly using Bonferroni t-interval. Comment on the same.

Explanation

(i)

Test the null and alternative hypothesis is

H 0 : There is no difference in the means of conductivity due to coaching type:

H 1 : At least one mean is different from others.

Assume that the testing of hypothesis at 0.05 level of significance.

Given that

… (168 more words) …

Question number: 11

» Multivariate Analysis » Estimation » Covariance Matrix

Edit

Appeared in Year: 2014

Essay Question▾

Describe in Detail

Let ,

Find ρ such that X 1 +X 2 +X 3 and X 1 -X 2 -X 3 are independent.

Explanation

Let

Given that Y and Z are independent, So

… (87 more words) …

Question number: 12

» Estimation » Optimal Properties » Sufficient Estimator

Edit

Appeared in Year: 2014

Essay Question▾

Describe in Detail

Show that is not a sufficient estimator of the Bernoulli parameter θ.

Explanation

Let X i is a ith random variable follows Bernoulli distribution with parameter θ. Then, the random variable is defined as

For i = 1,2, …, n

Now

So, th

… (94 more words) …