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

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## Question number: 8

» Hypotheses Testing » Hypothesis » Composite

Appeared in Year: 2014

### 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=

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## Question number: 9

» Hypotheses Testing » Randomised Test

Appeared in Year: 2014

### 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 pre

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## Question number: 10

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

Appeared in Year: 2014

### 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

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## Question number: 11

» Multivariate Analysis » Estimation » Covariance Matrix

Appeared in Year: 2014

### 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

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## Question number: 12

» Estimation » Optimal Properties » Sufficient Estimator

Appeared in Year: 2014

### 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, the pmf of Z is

e conditional distribution of

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