# For a sample of 12 college foo

For a sample of 12 college football playes the mean heart rateafter a morning workout session was 86 beats per minute and thestandard deviation of the sample was 8. find the 90% confidenceinterval of the true mean for all college football players after aworkout session

Solution :

Given that,

= 86

s = 8

n = 12

Degrees of freedom = df = n – 1 = 12 – 1 = 13

At 90% confidence level the t is ,

= 1 – 90% = 1 – 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t/2,df = t0.05,11 =1.796

Margin of error = E = t/2,df* (s /$\sqrt$n)

= 1.796 * (8/ $\sqrt$12) = 4.15

The 90% confidence interval Is

– E < < + E

86 – 4.15 < < 86 + 4.15

81.85 < < 90.15

(81.85,90.15)

90% confidence interval of the true mean for all collegefootball players after a workoutsession  (81.85,90.15)

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