Question

A machine is designed to fill 16-ounce bottles of shampoo. When the machine is working properly, the mean amount poured into the bottles is 16.05 ounces with a standard deviation of .005 ounces.

If four bottles are randomly selected each hour and the number of ounces in each bottle is measured, then 95% of the observations should occur in what interval? Round answers to four decimal places.

Answer 1

Solution :

Given that,

= 16.05 ounces

s = 0.005 ounce

n = 4

Degrees of freedom = df = n - 1 = 4-1=3

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,3 =3.182

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

= 3.182* (0.005 / 4) = 0.0087

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

- E < < + E

16.05 - 0.0087< < 16.05 + 0.0087

16.0413 < < 16.0587