Question

The winning team's scores in 11 highschool basketball games were recorded. If the sample mean is 10.5 points and the sample standard deviation is 0.25 points, find the 98% confidence interval of the true mean.

Answer 1

Solution :

Given that,

= 10.5

s =0.25

n =11

Degrees of freedom = df = n - 1 = 11- 1 = 10

At 98% confidence level the t is

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02/ 2 = 0.01

t /2,df = t0.01,10 = 2.764 ( using student t table)

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

= 2.764 * ( 0.25/ 11)

E = 0.2083

The 98% confidence interval estimate of the population mean is,

- E < < + E

10.5 - 0.2083< <10.5 + 0.2083

10.2917 < < 10.7083

( 10.2917 , 10.7083 )