1 -

A psychologist has developed a new test to measure sense of humor. The mean score on this test is found to be 55 in the population with a standard deviation of 12, and the scores form a normal distribution. A researcher would like to use this test to evaluate the theory that sense of humor changes as part of the aging process. To test this hypothesis, a sample of n = 26 people over 80 years old is obtained. The humor test is administered to each participant, and the mean score for the sample is 49. Do the data support the theory? Use = 0.05.

Part A - state the hypotheses

Part B - Create the decision rule. Include both the diagram/ picture and the critical region.

Part C - Calculate the test statistic for these data.

Part D - State your statistical decision (reject or fail to reject).

Part E - Interpret the outcome of the statistical test in terms of significance and how aging changes sense of humor

2-

Beth's friend Heather buys A LOT of shoes. In the last 10 years, Heather purchased a mean of 18 pairs per year. Last year she went really wild and purchased 24 pairs, corresponding to a z-score of +1.50. What is thestandard deviation of Heather's annual shoe indulgence? Show all of your work.

3 -

Let's say the mean number of flavors in Phoenix ice cream stores is 20, and the standard deviation is 4. What percent of ice cream stores havemore than 25 flavors? Show all of your work.

4 -

Suppose you have a population with a mean of = 42 and a standard deviation of = 40. You draw samples of size n = 100 from this distribution. What proportion of sample means will fall below M = 55?Be sure to show all of your work.

5 - Suppose you are screening individual people to participate in an experiment using an Attitude Scale with parameters of = 20 and = 3.5. You will select only people with scores between X = 24 and X = 26 to participate in your experiment.What proportion of people you screen will fall between X = 24 and X = 26.

Be sure to show all of your work (hint: draw the picture of the graph. You will need your Unit Normal Table)

5 -

Assume you are a career counselor; a client of yours has the scores given below on tests of interest in education, psychology, and retailing. Relative to the population, in which field does the client have most interest? Show any computations that are necessary to reach your conclusion. Then state your conclusion about what the highest interest area is for the client (is it Education, Psychology, or Retail).

	Education	Psychology	Retail
Client's score	40	88	80
Population mean	28	93	60
Population standard deviation	9	15	19