According to National Geographic, 28% of Canadians are of British descent.27 Suppose 150 Canadians in Alberta are randomly selected and 185 Canadians in Ontario are randomly selected.
a. What is the probability that the sample proportion of those Canadians from Alberta of British descent is less than 0.23?
b. What is the probability that the sample proportion of those Canadians from Ontario of British descent is less than 0.23?
c. What is the probability that the sample proportion of those Canadians from both provinces is greater than 0.35?
Suppose a company is receiving a large shipment of peel-and-stick vinyl floor tiles. The manufacturer claims the proportion of defective floor tiles is 0.05. The company will select a random sample of 200 floor tiles, carefully inspect each, and determine whether it is defective. The acceptance sampling plan states: Accept the entire shipment if the sample proportion of defective tiles is 0.08 or less; otherwise, reject the entire shipment.
a. Find the probability of accepting the entire shipment if the true proportion of defective floor tiles is 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.10, 0.15.
b. Plot the probability of accepting the entire shipment (on the y axis) versus the true proportion of defective floor tiles (on the x axis). The resulting graph is the OC curve for the given acceptance sampling plan.