Question 1 For your dissertation, you obtained data on the number of food products that twelve random customers bought at your local WeightRose store. The results are as follows:

1

3

2

3

12

3

5

9

8

6

2

4

a. What is the mean and median number of food products bought by these customers? (5 marks) b. Based on your answer under (a), and considering the mode, describe the shape of the distribution of these data. (5 marks) The sample standard deviation is (approximately) 3.33. c. Give the 95% confidence interval for the number of food products that these twelve individual customers bought. (5 marks) d. What does this confidence interval tell us about the average number of food products bought within the overall customer population at this particular WeightRose store? (5 marks) You would like to draw a random sample of customers so that the probability that the sample mean is within plus or minus one unit of the population mean equals 0.95. e. What is the minimum sample size that will satisfy this criterion? (5 marks)

Question 2 An independent motion picture company is interested in understanding the age profile of its online DVD customers buying the internationally acclaimed motion picture entitled “Bulb Friction”, starring the award-winning Jack L. Samuelson. The responsible marketing manager expects that the average age of these customers is at most 20 years. a. Formulate the null and alternative hypotheses that can be used to test this expectation. (5 marks) He subsequently draws a random sample of 144 customers buying the motion picture and he obtains a sample mean of 20.88 and a sample standard deviation of 4.6. b. Using the p-value to assess significance against α = 0.01, should the null hypothesis be rejected? (5 marks) c. Using a 95% confidence interval to conduct the hypothesis test, should the null hypothesis be