# ISS (Statistical Services) Statistics Paper II (Old Subjective Pattern): Questions 9 - 13 of 39

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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

## 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

## 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

## 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 (X _{1 }, X _{2 }, …, X

## Question number: 13

» Statistical Quality Control » Control Charts » Attributes

Appeared in Year: 2014

### Describe in Detail

Find 3-sigma control limits for a

(i) C-chart with process average equal to 4 non-conformities

(ii) U chart with process average c = 4, and n = 4.

### Explanation

the 3-sigma control limits is

(i) Given that

Control limits for the C chart with a known non-conformities is

(ii) Given that c = 4 and n = 4

Control limits for the U chart is