Question

. The winning team's scores in 13 high school basketball games were recorded. If the sample gave a mean of 10.5 points with a sample standard deviation of 0.25 points, find the 98% confidence interval of the true mean. Interpret the confidence interval.

Point Estimate: ______

Critical Value:

Margin of Error: ________

Confidence Interval: __________________________________________________

Interpretation: _______________________________________________

Answer 1

Solution :

Given that,

point estimate = 10.5

s =0.25

n =133

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

a ) At 98% confidence level the t is

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02/ 2 = 0.01

Critical Value t _/2,df = t_0.01,12 =2.681 ( using student t table)

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

=2.681 * (0.25 / 13)

E=0.1859

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

- E < < + E

10.5 - 0.1859 < < 10.5+ 0.1859

10.3141 < < 10.6859

(10.3141 ,10.6859 )