A postmix beverage machine is adjusted to release a certain

A postmix beverage machine is adjusted to release a certain amount of syrup into a chamber where it is mixed with carbonated water. A random sample of 25 beverages was found to have a mean syrup content of X = 1.14 fluid ounces and the sample standard deviation is S = 0.011 fluid ounces. Find a 95% two-sided confidence interval on the mean volume dispensed. (Round your answers to 3 decimal places.) Calculate the 95% two-sided confidence interval on the true mean volume dispensed. (

Solution

The degree of freedom =n-1=25-1=24

Given a=1-0.95=0.05, t(0.025, df=24) =2.06 (from student t table)

So the lower bound is

xbar - t*s/vn =1.14 -2.06*0.011/sqrt(25) =1.135

So the upper bound is

xbar + t*s/vn =1.14 +2.06*0.011/sqrt(25) =1.145