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Part (c) For the correct choice of the test given above, and any possible value of k = {0, 1,..., 15), find the probability of committing type II error if the true proportion of late deliveries is p = [0, 1]. To do that create a function ptypeIerr(p, k), with input parameters p and k which for any input value k returns ptypeIIerr(p,k) = P(type II error if the critical value is k) = probability of commiting type II error if the true proportion is p and the critical value of the test is k. Do NOT round your answer! Note: your function should assume any possible input of p = [0, 1] and any possible integer k = {0, 1, ..., 15}. You do not need to worry about values of p and k outside these ranges. Hint: just like with type I error, one line of a code inside the function may be sufficient here as well, if you apply (p<=0.2)* + (p>0.2)* . And again, if you feel more comfortable applying if...else statement to treat various values of p, that's also fine. In addition, make sure you know the meaning of lower.tail parameter for either of its values TRUE and FALSE. A fabric manufacturer believes that the proportion p of orders arriving late from a certain supplier of raw material exceeds 20%. To test this claim, the manufacturer collects a sample of 15 orders and records X = the number of orders in the sample that had been late. You can assume the orders are independent of each other, in terms of tardiness. The manufacturer wants to bring this problem up and confront the supplier only if they are certain in the claim with significance level of at most 10%. Part (a) Which of the following tests may the manufacturer perform for this purpose? p > 0.2; critical region: X0.2; critical region: Xk for some k € Z. p < 0.2; critical region: X ≤ k for some k Є Z 1. Ho 2. Ho 3. Ho p≤0.2 vs. Ha p≤0.2 vs. Ha p≥ 0.2 vs. Ha 4. Ho p≥ 0.2 vs. Ha p < 0.2; critical region: X > k for some k EZ 5. Ho p=0.2 vs. Ha p0.2; critical region: X k2 k2 6. Ho p = 0.2 vs. Ha p 0.2; critical region: k₁ ≤ X ≤ k₂ for some k₁, k₂ E Z. 7. None of the above

Part (c) For the correct choice of the test given above, and any possible value of k = {0, 1,..., 15), find the probability of committing type II error if the true proportion of late deliveries is p = [0, 1]. To do that create a function ptypeIerr(p, k), with input parameters p and k which for any input value k returns ptypeIIerr(p,k) = P(type II error if the critical value is k) = probability of commiting type II error if the true proportion is p and the critical value of the test is k. Do NOT round your answer! Note: your function should assume any possible input of p = [0, 1] and any possible integer k = {0, 1, ..., 15}. You do not need to worry about values of p and k outside these ranges. Hint: just like with type I error, one line of a code inside the function may be sufficient here as well, if you apply (p<=0.2)* + (p>0.2)* . And again, if you feel more comfortable applying if...else statement to treat various values of p, that's also fine. In addition, make sure you know the meaning of lower.tail parameter for either of its values TRUE and FALSE. A fabric manufacturer believes that the proportion p of orders arriving late from a certain supplier of raw material exceeds 20%. To test this claim, the manufacturer collects a sample of 15 orders and records X = the number of orders in the sample that had been late. You can assume the orders are independent of each other, in terms of tardiness. The manufacturer wants to bring this problem up and confront the supplier only if they are certain in the claim with significance level of at most 10%. Part (a) Which of the following tests may the manufacturer perform for this purpose? p > 0.2; critical region: X0.2; critical region: Xk for some k € Z. p < 0.2; critical region: X ≤ k for some k Є Z 1. Ho 2. Ho 3. Ho p≤0.2 vs. Ha p≤0.2 vs. Ha p≥ 0.2 vs. Ha 4. Ho p≥ 0.2 vs. Ha p < 0.2; critical region: X > k for some k EZ 5. Ho p=0.2 vs. Ha p0.2; critical region: X k2 k2 6. Ho p = 0.2 vs. Ha p 0.2; critical region: k₁ ≤ X ≤ k₂ for some k₁, k₂ E Z. 7. None of the above

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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Part (c) For the correct choice of the test given above, and any possible value of k = {0, 1,..., 15), find the probability of committing type II error if the true proportion of late deliveries is p = [0, 1]. To do that create a function ptypeIerr(p, k), with input parameters p and k which for any input value k returns ptypeIIerr(p,k) = P(type II error if the critical value is k) = probability of commiting type II error if the true proportion is p and the critical value of the test is k. Do NOT round your answer! Note: your function should assume any possible input of p = [0, 1] and any possible integer k = {0, 1, ..., 15}. You do not need to worry about values of p and k outside these ranges. Hint: just like with type I error, one line of a code inside the function may be sufficient here as well, if you apply (p<=0.2)*<something> + (p>0.2)*<something else> . And again, if you feel more comfortable applying if...else statement to treat various values of p, that's also fine. In addition, make sure you know the meaning of lower.tail parameter for either of its values TRUE and FALSE.
Transcribed Image Text:Part (c) For the correct choice of the test given above, and any possible value of k = {0, 1,..., 15), find the probability of committing type II error if the true proportion of late deliveries is p = [0, 1]. To do that create a function ptypeIerr(p, k), with input parameters p and k which for any input value k returns ptypeIIerr(p,k) = P(type II error if the critical value is k) = probability of commiting type II error if the true proportion is p and the critical value of the test is k. Do NOT round your answer! Note: your function should assume any possible input of p = [0, 1] and any possible integer k = {0, 1, ..., 15}. You do not need to worry about values of p and k outside these ranges. Hint: just like with type I error, one line of a code inside the function may be sufficient here as well, if you apply (p<=0.2)*<something> + (p>0.2)*<something else> . And again, if you feel more comfortable applying if...else statement to treat various values of p, that's also fine. In addition, make sure you know the meaning of lower.tail parameter for either of its values TRUE and FALSE.
A fabric manufacturer believes that the proportion p of orders arriving late from a certain supplier of raw material exceeds 20%. To test this claim, the manufacturer collects a sample of 15 orders and records X = the number of orders in the sample that had been late. You can assume the orders are independent of each other, in terms of tardiness. The manufacturer wants to bring this problem up and confront the supplier only if they are certain in the claim with significance level of at most 10%. Part (a) Which of the following tests may the manufacturer perform for this purpose? p > 0.2; critical region: X<k for some kЄ Z. p>0.2; critical region: Xk for some k € Z. p < 0.2; critical region: X ≤ k for some k Є Z 1. Ho 2. Ho 3. Ho p≤0.2 vs. Ha p≤0.2 vs. Ha p≥ 0.2 vs. Ha 4. Ho p≥ 0.2 vs. Ha p < 0.2; critical region: X > k for some k EZ 5. Ho p=0.2 vs. Ha p0.2; critical region: X <k₁ or X k₂ for some k₁, k₂ € Z. : > k2 k2 6. Ho p = 0.2 vs. Ha p 0.2; critical region: k₁ ≤ X ≤ k₂ for some k₁, k₂ E Z. 7. None of the above
Transcribed Image Text:A fabric manufacturer believes that the proportion p of orders arriving late from a certain supplier of raw material exceeds 20%. To test this claim, the manufacturer collects a sample of 15 orders and records X = the number of orders in the sample that had been late. You can assume the orders are independent of each other, in terms of tardiness. The manufacturer wants to bring this problem up and confront the supplier only if they are certain in the claim with significance level of at most 10%. Part (a) Which of the following tests may the manufacturer perform for this purpose? p > 0.2; critical region: X<k for some kЄ Z. p>0.2; critical region: Xk for some k € Z. p < 0.2; critical region: X ≤ k for some k Є Z 1. Ho 2. Ho 3. Ho p≤0.2 vs. Ha p≤0.2 vs. Ha p≥ 0.2 vs. Ha 4. Ho p≥ 0.2 vs. Ha p < 0.2; critical region: X > k for some k EZ 5. Ho p=0.2 vs. Ha p0.2; critical region: X <k₁ or X k₂ for some k₁, k₂ € Z. : > k2 k2 6. Ho p = 0.2 vs. Ha p 0.2; critical region: k₁ ≤ X ≤ k₂ for some k₁, k₂ E Z. 7. None of the above
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