Annabel, a retail analyst, has been following Under Armour, Inc., the pioneer in the compressiongear market. Compression garments are meant to keep moisture away from a wearer's body during athletic activities in warm and cool weather. Annabel believes that the Under Armour brand attracts a younger customer, whereas the more established companies, Nike and Adidas, draw an older clientele. In order to test her belief, she collects data on the age of the customers and whether or not they purchased Under Armour (1 for Under Armour, 0 otherwise). A portion of the data is shown in the accompanying table.

Under Armour........... Age

1.............................30

0.............................19

⋮ ..............................⋮

1............................ 24

a. Estimate a linear probability model using Under Armour as the response variable and age as the explanatory variable.

b. Compute the predicted probability of an Under Armour purchase for a 20-year-old customer and a 30-year-old customer.

c. Test Annabel's belief that the Under Armour brand attracts a younger customer at the 5% level.