The z-test

Assignment #10 
The z-test 
10.1 Assume that a treatment does have an effect and that the treatment effect is being evaluated with a z hypothesis test.  If all factors are held constant, how is the outcome of the hypothesis test influenced by sample size?  To answer this question, do the following two tests and compare the results.  For both tests, a sample is selected from a normal population distribution with a mean of μ = 60 and a standard deviation of  σ = 10.  After the treatment is administered to the individuals in the sample, the sample mean if found to be M = 65.  In each case, use a two-tailed test with  = .05. a. For the first test, assume that the sample consists of n = 4 individuals. b. For the second test, assume that the sample consists of n = 25 individuals. c. Explain in your own words how the outcome of the hypothesis test is influenced by the sample size.
Note: Be sure and show a picture of the research design.  Also show all steps and calculations you made for each test following the process outlined in the z-test formula sheet handout.  What statistical decision do you make in each case? 
10.2 Researchers have often noted increases in violent crimes when it is very hot.  In fact, Reifman, Larrick, and Fein (1991) noted that this relationship even extends to baseball.  That is, there is a much greater chance of a batter being hit by a pitch when the temperature increases.  Consider the following hypothetical data.  Suppose that over the past 30 years, during any given week of the major league season, an average of μ = 12 players are hit by wild pitches.  Assume the distribution is nearly normal with σ = 3.  For a sample of n = 4 weeks in which the daily temperature was extremely hot, the weekly average of hit-by-pitch players was M = 15.5.  Are players more likely to get hit by pitches during the hot weeks?  Set alpha to .05 for a one-tailed test.