1. 

In each of the following situations, a significance test for a population mean µ is called for. State the null hypothesis H0 and the alternative hypothesis  Ha in each case. Then, describe in context what constitutes a Type I error and what constitutes a Type II error.

a) Experiments on learning in animals sometimes measure how long it takes a mouse to find its way through a maze. The mean time is 18 seconds for one particular maze. A researcher thinks that a loud noise will cause the mice to complete the maze faster. She measures how long each of 10 mice takes with a noise as stimulus.
b) The examinations in a large history class are scaled after grading so that the mean score is 50. A self-confident teaching assistant thinks that his students have a higher mean score than the class as a whole. His students this semester can be considered a sample from the population of all students he might teach, so he compares their mean score with 50.
c) The Census Bureau reports that households spend an average of 31% of their total spending on housing. A homebuilders association in Cleveland wonders if the national finding applies in their area. They interview a sample of 40 households in the Cleveland metropolitan area to learn what percent of their spending goes toward housing.

You have an SRS of size n = 9 from a normal distribution with σ=9 . You wish to test
 H0 μ =0

Ha μ >0
You decide to reject  if x > 0 and to accept H₀ otherwise.

a) Find the probability of a Type I error.
b) Describe a Type II error.

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