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f(x; 0) = (0*(1 - 0)¹-x, x = 0,1. 0, otherwise where 0 < 0 ≤ is a parameter. The hypothesis Ho: 0 = to be tested against 2 H₁: p < 1/1/ i) If Ho is rejected when X₁ ≤ 6. then what is the probability of type I error? the probability of type Lerror?

f(x; 0) = (0*(1 - 0)¹-x, x = 0,1. 0, otherwise where 0 < 0 ≤ is a parameter. The hypothesis Ho: 0 = to be tested against 2 H₁: p < 1/1/ i) If Ho is rejected when X₁ ≤ 6. then what is the probability of type I error? the probability of type Lerror?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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2/2 1) Let X₁, X₂, ..., X20 be a random sample from a population X with density (0* (1 - 0)¹-x, x = 0,1. 0, otherwise f(x; 0) = 100% where 0 < 0 ≤ is a parameter. The hypothesis Ho: 0= to be tested against H₁: p < / i) If Ho is rejected when X₁ ≤ 6. then what is the probability of type I error? ii) If Ho is rejected when Σ2₁ X¡ ≤ 6. then what is the probability of type I error? 2) A new quality assurance process developed in Limpopo by Mr Masela for a newly introduced Sephaku Cement results in a mean strength of 5000 with a standard deviation of 120 kilograms. In order for Mr Masela to test the null hypothesis that μ = 5000 against the alternative that µ< 5000, He random sampled 50 fragments of this cement and tested them. If his critical region was defined to be y < 4970. What will be his probability of not committing type II error when μ = 4960.
Transcribed Image Text:2/2 1) Let X₁, X₂, ..., X20 be a random sample from a population X with density (0* (1 - 0)¹-x, x = 0,1. 0, otherwise f(x; 0) = 100% where 0 < 0 ≤ is a parameter. The hypothesis Ho: 0= to be tested against H₁: p < / i) If Ho is rejected when X₁ ≤ 6. then what is the probability of type I error? ii) If Ho is rejected when Σ2₁ X¡ ≤ 6. then what is the probability of type I error? 2) A new quality assurance process developed in Limpopo by Mr Masela for a newly introduced Sephaku Cement results in a mean strength of 5000 with a standard deviation of 120 kilograms. In order for Mr Masela to test the null hypothesis that μ = 5000 against the alternative that µ< 5000, He random sampled 50 fragments of this cement and tested them. If his critical region was defined to be y < 4970. What will be his probability of not committing type II error when μ = 4960.
Expert Solution
Step 1

Given

X~Ber(1,θ)

nCr=n!/(r!(n-r)!)

r!=r(r-1)(r-2)....3×2×1

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