Psychology 60, Fall 2016 Name: ______________________________________ Homework #5 ID#: ________________________________________ Due in class Tuesday, November 8th T.A. & Section time: ____________________________ Homework must be stapled, legible, and handed in before the beginning of lecture on the date indicated above. If you fail to turn in a homework, or turn it in late, you will receive zero points. 1) Define the sampling distribution of the mean (1 pt). 2) What does the central limit theorem tell us? Both parts. (2pt). 3) What are the conditions/assumptions necessary to run a Z-test? (1 pt.) 4) Consider randomly sampling from a theoretical normal distribution (and remember symmetry implications). Hint: each randomly sampled observation is statistically independent of the other randomly sampled observation. (1 pt. each). a. b. c. d. What is the probability that a single randomly sampled observation have a value above the mean? What is the probability that observations from a random sample size of n=2 will both have values above the mean? What is the probability that observations from a random sample size of n=4 will all have values above the mean? What is the probability that observations from a sample size of n=8 will all have values above the mean? 5) How do the probabilities in question 4 provide insight into the fact that the standard error of a sampling distribution decreases as sample size increases? (2 pts.) 6) (10 pts) Way back in the olden days, Blockbuster tallied all their US movie rental data and found that on average, individuals rent 10 movies a year with a standard deviation of 3. Treat these as population statistics. They wanted to see if movie rental rates in Yuma, Arizona, were different from those of the country as a whole (why Yuma? Who knows ). A random sample of 25 blockbuster members in Yuma yielded a mean rental rate of 11.3 movies per year. a. State the null and alternative hypotheses b. State the decision rule c. Calculate the test statistic d. State the decision (retain or reject Ho) e. Interpret the results f. State whether and why necessary assumptions are met