(Solution) - A random sample of 400 voters in a certain city -(2025 Original AI-Free Solution)

Paper Details

A random sample of 400 voters in a certain city are asked if they favor an additional 4% gasoline sales tax to provide badly needed revenues for street repairs. If more than 220 but fewer than 260 favor the sales tax, we shall conclude that 60% of the voters are for it.
(a) Find the probability of committing a type I error if 60% of the voters favor the increased tax.
(b) What is the probability of committing a type II error using this test procedure if actually only 48% of the voters are in favor of the additional gasoline tax?