A shoe manufacturer claims that athletes can increase their vertical jump heights using the manufacturer's training shoes. The vertical jump heights of eight randomly selected athletes are measured. After the athletes have used the shoes for 10 months, their vertical jump heights are measured again. The vertical jump heights (in inches) for each athlete and some statistics are given in the table below. Athlete 1 2 3 4 5 6 7 8 Mean SD jump height before using the shoes 24 26 26 22 30 22 20 31 25.1250 3.9074 jump height after using the shoes 27 30 27 24 29 24 23 33 27.1250 3.4408 difference 3 4 1 2 - 1 2 3 2 2.0000 1.5119 Where difference = jump height after shoes - jump height before shoes. At a = 0.10, is there enough evidence to support the manufacurer's claim? Assume the vertical jump heights are normally distributed. 1. Null hypothesis, Ud = Hafter - Hbefore OHd > 0 Oa zo OHd = 0 Od =0 O Hd = 0 OHd 0 Od =0 OHd = 0 OHd = 0 o