Part (b) For the correct choice of the test given above, and any possible value of k = {0,1,..., 15), find the probability of committing type I error if the true proportion of late deliveries is pЄ [0, 1]. To do that create a function ptypeIerr (p,k), with input parameters p and k which for any input value k returns ptypeIerr(p,k) = P(type I error if the critical value is k) = probability of commiting type I 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 one line of a code inside the function may be sufficient, if you apply (p<=0.2)* + (p>0.2)*. This is because logical values TRUE and FALSE, when multiplied by numeric values, get coerced into 1 and 0, respectively, before multiplied with the numeric value. If you feel more comfortable applying if...else statement to treat various values of p, that's also fine. Also, when applying appropriate R function, read the documentation about values of lower.tail parameter and their meanings. Keep in mind that for a discrete random variable X, in general, P(X ≤k) P(X k). 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 (b) For the correct choice of the test given above, and any possible value of k = {0,1,..., 15), find the probability of committing type I error if the true proportion of late deliveries is pЄ [0, 1]. To do that create a function ptypeIerr (p,k), with input parameters p and k which for any input value k returns ptypeIerr(p,k) = P(type I error if the critical value is k) = probability of commiting type I 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 one line of a code inside the function may be sufficient, if you apply (p<=0.2)* + (p>0.2)*. This is because logical values TRUE and FALSE, when multiplied by numeric values, get coerced into 1 and 0, respectively, before multiplied with the numeric value. If you feel more comfortable applying if...else statement to treat various values of p, that's also fine. Also, when applying appropriate R function, read the documentation about values of lower.tail parameter and their meanings. Keep in mind that for a discrete random variable X, in general, P(X ≤k) P(X k). 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
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![Part (b)
For the correct choice of the test given above, and any possible value of k = {0,1,..., 15), find the probability of committing type I error if the true proportion
of late deliveries is pЄ [0, 1]. To do that create a function ptypeIerr (p,k), with input parameters p and k which for any input value k returns
ptypeIerr(p,k) = P(type I error if the critical value is k) = probability of commiting type I 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 one line of a code inside the function may be sufficient, if you apply
(p<=0.2)*<something> + (p>0.2)*<something else>.
This is because logical values TRUE and FALSE, when multiplied by numeric values, get coerced into 1 and 0, respectively, before multiplied with the numeric
value. If you feel more comfortable applying if...else statement to treat various values of p, that's also fine. Also, when applying appropriate R function,
read the documentation about values of lower.tail parameter and their meanings. Keep in mind that for a discrete random variable X, in general,
P(X ≤k) P(X <k), and P(X ≥ k) + P(X > k).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe99fe633-2e82-4dde-a878-82e2251a369a%2F2d301ab8-d790-4341-99f4-32a6e6026411%2Ftzjr1t_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Part (b)
For the correct choice of the test given above, and any possible value of k = {0,1,..., 15), find the probability of committing type I error if the true proportion
of late deliveries is pЄ [0, 1]. To do that create a function ptypeIerr (p,k), with input parameters p and k which for any input value k returns
ptypeIerr(p,k) = P(type I error if the critical value is k) = probability of commiting type I 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 one line of a code inside the function may be sufficient, if you apply
(p<=0.2)*<something> + (p>0.2)*<something else>.
This is because logical values TRUE and FALSE, when multiplied by numeric values, get coerced into 1 and 0, respectively, before multiplied with the numeric
value. If you feel more comfortable applying if...else statement to treat various values of p, that's also fine. Also, when applying appropriate R function,
read the documentation about values of lower.tail parameter and their meanings. Keep in mind that for a discrete random variable X, in general,
P(X ≤k) P(X <k), and P(X ≥ k) + P(X > k).
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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