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The question is...

1. A coach uses a new technique in training middle distance runners. The times for 8 different athletes
to run 800 meters before and after this training are shown below.

Athlete

A

B

C

D

E

F

G

H

Time before

training (seconds)

116

115.9

118.6

109.7

111.5

113

119

116

Time after training

(seconds)

116.6

114.6

116.2

110.5

109.7

113.1

115.4

112.1

Using a 0.05 level of significance, test the claim that the training helps to improve the athletes' times for the 800 meters (note: x-bar for the differences is 1.4375, and s for the differences is  1.8260).

Test statistic t = 2.227. Critical value: t = 1.895.
Reject H0: μd ≤ 0. There is sufficient evidence to support the claim that the training helps to improve the athletes' times for the 800 meters.