# Hypotheses Testing (ISS (Statistical Services) Statistics Paper II (Old Subjective Pattern)): Questions 1 - 6 of 9

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## Question number: 1

» Hypotheses Testing » Likelihood Ratio Test » ASN Function

Appeared in Year: 2015

### Describe in Detail

Derive the likelihood ratio test for comparing the means of k independent homoscedastic normal populations.

### Explanation

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## Question number: 2

» 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

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## Question number: 3

» 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

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## Question number: 4

» Hypotheses Testing » Likelihood Ratio Test » ASN Function

Appeared in Year: 2014

### Describe in Detail

x _{1 }, x _{2 }, …, x _{n } is a random sample from N (θ, σ ^{2 }) (σ ^{2 } not specified). Derive likelihood ratio test of testing H _{0 }: θ=θ _{0 } against H _{1 }: θ ≠ θ _{0 }.

### Explanation

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## Question number: 5

» Hypotheses Testing » Two Kinds of Error

Appeared in Year: 2014

### Describe in Detail

A single observation of a r. v. having a geometric distribution with pmf

The null hypothesis is H _{0 }: θ=0.5 against the alternative hypothesis H _{1 }: θ=0.6 is rejected if the observed value of r. v. is greater than equal to 5. Find the probabilities of type I error and type II error.

### Explanation

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## Question number: 6

» Hypotheses Testing » Randomised Test

Appeared in Year: 2014

### Describe in Detail

chart is used to control the mean of normally distributed characteristic. It is know that . The center line is 200. If the process mean shifts to 188, find the probability that this shift is detected on the first subsequent sample.

### Explanation

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