You are conducting quality control for a company that manufactures LED displays. The factory you are assessing is supposed to have a manufacturing defect rate of 1 in 100 LED displays. As part of your assessment, you want to verify this defect rate by analyzing a random sample of LED displays. You are planning to randomly sample 1500 displays from this factory and observe how many of them contain manufacturing defects. Let Zi be equal to 1 if the i’th display has a defect and 0 otherwise, for i = 1,...,1500. (a) What is the statistic that you will use to estimate the defect rate for this factory? How do you compute it using Z1, Z2, . . . , Z1500? (b) Assuming that the true defect rate for this factory is in fact 1 in 100 displays, can we approximate the sampling distribution of the statistic that you selected in part (a) using a normal distribution? Please state and check the requirements for applying the approximation, and identify the mean and standard deviation of the normal distribution. (c) What is the chance that your randomly drawn sample is such that your sample statistic from (a) is lower than 0.015?
You are conducting quality control for a company that manufactures LED displays. The factory you are assessing is supposed to have a manufacturing defect rate of 1 in 100 LED displays.
As part of your assessment, you want to verify this defect rate by analyzing a random sample of LED displays. You are planning to randomly sample 1500 displays from this factory and observe how many of them contain manufacturing defects. Let Zi be equal to 1 if the i’th display has a defect and 0 otherwise, for i = 1,...,1500.
(a) What is the statistic that you will use to estimate the defect rate for this factory? How do you compute it using Z1, Z2, . . . , Z1500?
(b) Assuming that the true defect rate for this factory is in fact 1 in 100 displays, can we approximate the sampling distribution of the statistic that you selected in part (a) using a
(c) What is the chance that your randomly drawn sample is such that your sample statistic from (a) is lower than 0.015?
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
