Question

Ten Mile Run ~ A random sample of 50 runners from all the runners who finished the Cherry Blossom Ten Mile Run in 2009 had a mean finishing time 94.5 minutes and a standard deviation of 18.5 minutes. What is the lower bound for a 95% confidence interval for the actual mean finishing time? Give your answer to 4 decimal places

Answer 1

Solution :

degrees of freedom = n - 1 = 50 - 1 = 49

t,df = t_0.05,49 = 1.677

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

= 1.677 * (18.5 / 50)

Margin of error = E = 4.3875

The 95% lower confidence interval estimate of the population mean is,

- E  

= 94.5 - 4.3875 = 90.1125

lower bound = 90.1125