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I have a loaded die which shows number 6 four times more often than a fair die does. We want to play a game, but you don't know whether I am using the loaded die or a fair one. You suspect I am cheating. However, that's a strong statement and you want to test it, and accuse me of cheating only if you have enough evidence. So, you would want to test Ho: 0= vs. HA: 0= = To test this, suppose you are allowed to cast a die as many times as needed until 6 appears for the first time (and then you stop). So, you use the statistic X = number of casts of the die until 6 appears as an outcome (for the first time). Note that if the die is loaded you would expect to wait less, i.e. cast the die smaller number of times until 6 appears for the first time. Which of these sets C is the most reasonable choice for critical (i.e. rejection) region? Also, for the right choice of the critical region, how would you find type I error a = probability of (incorrectly) rejecting Ho when it is actually true? Check all that applies. Hint: think about what values x (= number of casts until 6 appears for the first time) would give you a good evidence that the die is loaded, and what values the die is more likely to be fair. would be evidence that Po (k≤ X ≤ k₂) □ P(X≥k) C={x N|xk} for some appropriate value k Є N. □ P(X ≤k) OC= {xЄN|x < k} for some appropriate value kЄ N. □ α = P(X ≤k) □ α = P(X ≥k) OC={EN|k1 < x < k2} for some appropriate values k1, k2 € N.

I have a loaded die which shows number 6 four times more often than a fair die does. We want to play a game, but you don't know whether I am using the loaded die or a fair one. You suspect I am cheating. However, that's a strong statement and you want to test it, and accuse me of cheating only if you have enough evidence. So, you would want to test Ho: 0= vs. HA: 0= = To test this, suppose you are allowed to cast a die as many times as needed until 6 appears for the first time (and then you stop). So, you use the statistic X = number of casts of the die until 6 appears as an outcome (for the first time). Note that if the die is loaded you would expect to wait less, i.e. cast the die smaller number of times until 6 appears for the first time. Which of these sets C is the most reasonable choice for critical (i.e. rejection) region? Also, for the right choice of the critical region, how would you find type I error a = probability of (incorrectly) rejecting Ho when it is actually true? Check all that applies. Hint: think about what values x (= number of casts until 6 appears for the first time) would give you a good evidence that the die is loaded, and what values the die is more likely to be fair. would be evidence that Po (k≤ X ≤ k₂) □ P(X≥k) C={x N|xk} for some appropriate value k Є N. □ P(X ≤k) OC= {xЄN|x < k} for some appropriate value kЄ N. □ α = P(X ≤k) □ α = P(X ≥k) OC={EN|k1 < x < k2} for some appropriate values k1, k2 € N.

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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I have a loaded die which shows number 6 four times more often than a fair die does. We want to play a game, but you don't know whether I am using the loaded die or a fair one. You suspect I am cheating. However, that's a strong statement and you want to test it, and accuse me of cheating only if you have enough evidence. So, you would want to test Ho: 0= vs. HA: 0= = To test this, suppose you are allowed to cast a die as many times as needed until 6 appears for the first time (and then you stop). So, you use the statistic X = number of casts of the die until 6 appears as an outcome (for the first time). Note that if the die is loaded you would expect to wait less, i.e. cast the die smaller number of times until 6 appears for the first time. Which of these sets C is the most reasonable choice for critical (i.e. rejection) region? Also, for the right choice of the critical region, how would you find type I error a = probability of (incorrectly) rejecting Ho when it is actually true? Check all that applies. Hint: think about what values x (= number of casts until 6 appears for the first time) would give you a good evidence that the die is loaded, and what values the die is more likely to be fair. would be evidence that
Transcribed Image Text:I have a loaded die which shows number 6 four times more often than a fair die does. We want to play a game, but you don't know whether I am using the loaded die or a fair one. You suspect I am cheating. However, that's a strong statement and you want to test it, and accuse me of cheating only if you have enough evidence. So, you would want to test Ho: 0= vs. HA: 0= = To test this, suppose you are allowed to cast a die as many times as needed until 6 appears for the first time (and then you stop). So, you use the statistic X = number of casts of the die until 6 appears as an outcome (for the first time). Note that if the die is loaded you would expect to wait less, i.e. cast the die smaller number of times until 6 appears for the first time. Which of these sets C is the most reasonable choice for critical (i.e. rejection) region? Also, for the right choice of the critical region, how would you find type I error a = probability of (incorrectly) rejecting Ho when it is actually true? Check all that applies. Hint: think about what values x (= number of casts until 6 appears for the first time) would give you a good evidence that the die is loaded, and what values the die is more likely to be fair. would be evidence that
Po (k≤ X ≤ k₂) □ P(X≥k) C={x N|xk} for some appropriate value k Є N. □ P(X ≤k) OC= {xЄN|x < k} for some appropriate value kЄ N. □ α = P(X ≤k) □ α = P(X ≥k) OC={EN|k1 < x < k2} for some appropriate values k1, k2 € N.
Transcribed Image Text:Po (k≤ X ≤ k₂) □ P(X≥k) C={x N|xk} for some appropriate value k Є N. □ P(X ≤k) OC= {xЄN|x < k} for some appropriate value kЄ N. □ α = P(X ≤k) □ α = P(X ≥k) OC={EN|k1 < x < k2} for some appropriate values k1, k2 € N.
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