A paint manufacturer claims that its brand of interior latex paint will cover, on average, at least 400 square feet per gallon. A consumer group is to test this claim. They are going to use a random sample of 32 gallons of the paint and a 5% level of significance. Assume that the population standard deviation is known to be 40 square feet. What is the probability of making a Type II error if the actual true mean is 380 square feet?

I need to see a Null hypothesis, an Alternate hypothesis, your work to get a t or Z value, a critical value for the test, a Decision, and if asked, a Conclusion.