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# National Fitness Challenge

APSTAT-YLLPDN

Two large high schools are competing with each other in a national fitness challenge.

Five students are selected at random from each school. Their running times for a $5$-kilometer run, rounded to the nearest minute, is recorded below:

School A: $30, 35, 30, 32, 24$
Mean: $30.2$
Standard Deviation: $4.025$

School B: $27, 22, 36, 30, 31$
Mean: $29.2$
Standard Deviation: $5.167$

Determine the most exact value of a $95\%$ confidence interval for the difference of the two schools’ running times.

A

$(-2.72, 4.72)$

B

$(-4.49, 6.49)$

C

$(-5.76, 7.75)$

D

$(-5.83, 7.83)$

E

$(-9, 11)$