A manufacturer of plumbing fixtures has developed a new type of washerless faucet. Let rho-P(a randomly selected faucet of this type will develop a leak within 2 years under normal use). The manufacturer has decided to proceed with production unless it can be determined that p is too large; the borderline acceptable value of p is specified as 0.10. The manufacturer decides to subject n of these faucets to accelerated testing (approximating 2 years of normal use). with X = the number among the n faucets that leak before the test concludes, production will commence unless the observed X is too large. It is decided that if p = 0.10, the probability of not proceeding should be at most 0.10, whereas if rho = 0.30 the probability of proceeding should be at most 0.10. (Assume the rejection region takes the form reject H if X2 c for some c. Round your answers to three decimal places.) 1. What are the error probabilities for n10? P-value- Can n- 10 be used?
a. It is not possible to use n = 10 because there is no value of X which results in a P-value
b. It is not possible to use n10 because it results in B(0.3)> 0.1
c. It is not possible to use n 10 because it results in B(0.3)<0.1 0.1.
d. It is possible to use n = 10 because both the P-value and β(0.3) are less than 0.1
e. It is possible to use 10 because both the P-value and B(0.3) are greater than 0.1
What are the error probabilities for n-20? P-value = β(0-3) = Can n 20 be used?
a. It is not possible to use n = 20 because there is no value of X which results in a P-value
b. It is not possible to use n 20 because it results in B(0.3)0.1
c. It is not possible to use n 20 because it results in B(0.3) < 0.1
d. It is possible to use n 20 because both the P-value and B(0.3) are less than 0.1
e. It is possible to use n 20 because both the P-value and B(0.3) are greater than 0.1
2. What are the error probabilities for n-25? P-value . P(0.3) Can n 25 be used?
a. It is not possible to use n-25 because there is no value of X which results in a P-value
b. It is not possible to use n 25 because it results in B(o.3) > 0.1
c. It is not possible to use n 25 because it results in B(0.3) < 0.1
d. It is possible to use n 25 because both the P-value and B(0.3) are less than 0.1
e. It is possible to use n 25 because both the P-value and B(0.3) are greater than 0.1 0.1.