Question

For a sample of 12 college football playes the mean heart rate after a morning workout session was 86 beats per minute and the standard deviation of the sample was 8. find the 90% confidence interval of the true mean for all college football players after a workout session

Answer 1

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 = t_0.05,11 =1.796

Margin of error = E = t_/2,df * (s /n)

= 1.796 * (8/ 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 college football players after a workout session  (81.85,90.15)