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

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Question number: 6

» Hypotheses Testing » Randomised Test

Appeared in Year: 2014

Essay Question▾

Describe in Detail

X chart is used to control the mean of normally distributed characteristic. It is know that σ=6andn=4 . 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

Type II error is the probability of saying that the process is under control when it is not under control, that is, the probability of a point falling within control limits after the shift the mean. This is also known as the probability of not detecting the shift after shift… (177 more words) …

Question number: 7

» Hypotheses Testing » Most Powerful Test

Appeared in Year: 2014

Essay Question▾

Describe in Detail

Let X be r. v. with pmf under H 0 and H 1 given below. Find M. P. test with α=0.03

Possible X Values given in table

Finding a values of f 0 (x) and f 1 (x) to given a table.

x

1

2

3

4

5

6

f 0 (x)

0.01

0.01

0.01

0.01

0.01

0.95

f 1 (x)

0.05

0.04

0.03

0.02

0.01

0.85

Explanation

To find the M. P. test, first we compute

Z=f1(x)f0(x)

Calculate Z in given table

Finding a values of P (Z = Z) and Fz (z) to given a table.

Z

5

4

3

2

1

0.8947

The possible… (205 more words) …

Question number: 8

» Hypotheses Testing » Unbiased Test

Appeared in Year: 2015

Essay Question▾

Describe in Detail

Explain the notion of unbiasedness with regards to a test of a hypothesis. Examine the validity of the statement. A most powerful test is invariably unbiased.

Explanation

A test T of the null hypothesis H0:θϵΘ0vsH1:θϵΘ1 is said to be an unbiased test if the probability of rejection H 0 when it is false is at least as much as the probability of… (173 more words) …

Question number: 9

» Hypotheses Testing » Uniformly Most Powerful Test

Appeared in Year: 2015

Essay Question▾

Describe in Detail

Fins a Most powerful test for testing the simple hypothesis H0:σ2=σ02 against the simple alternative hypothesis H1:σ2=σ12 based on n random observations from N (µ, σ 2) where µ is know. Show that this MP test is UMP (Uniformly most powerful).

Explanation

Let X i ’s are n random observations from N (µ, σ 2) and the pdf is

f(x_)=(2πσ2)n2exp{12σ2i=1n(xi… (532 more words) …

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