Question

22) Runner's World magazine wanted to find out what the average 5k running time was for recreational runners. To estimate this, they took a random sample of 64 runner's times from a database of recreational 5k races across the country. This sample resulted in a sample mean (X) of 28 minutes with a sample standard deviation of 5 minutes. Calculate a 95% confidence interval around the mean. (5 points)

Answer 1

Solution :

Given that,

t_{$\alpha$ /2,df} = 1.998

Margin of error = E = t_{$\alpha$/2,df} * (s /$\sqrt$n)

= 1.998 * (5 / $\sqrt$ 64)

Margin of error = E = 1.2

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

$\bar x$ - E < $\mu$ < $\bar x$ + E

28 - 1.2 < $\mu$ < 28 + 1.2

26.8 < $\mu$ < 29.2

(26.8 , 29.2)