# Hypotheses Testing-Two Kinds of Error (ISS (Statistical Services) Statistics Paper II (Old Subjective Pattern)): Questions 1 - 1 of 1

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## Question number: 1

» 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

The type I error is the probability that reject H _{0 } when it is true denote by α and type II error is the probability that accept H _{0 } when it is false denote by β

Given that the null hypothesis is rejected if the observed value of r. v. is greater than equal to 5 that means X ≥ 5.

For type I error,

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