A researcher hypothesizes that people who have experienced trauma result in an increase in the number of dreams they can recall per month. The researcher knows that the population mean for the number of dreams that people are able to recall per month is 5, with a standard deviation of 4. The researcher randomly selects 36 individuals who have recently experienced a traumatic event, and record the number of dreams they can recall. The mean number of dreams recalled by the sample is 8.

a) state the null hypothesis; b) stated the alternate hypothesis; c) carry out a Z test at the 0.01 significance level (show your work), d) state if the difference between the sample mean and the population mean is significant or not, and explain why?; e) If the result is significant, find the effect size; f) is the effect size small, medium, or large? Why?