Question

A soda bottling plant fills cans labeled to contain 12 ounces of soda. The filling machine varies and does not fill each can with exactly 12 ounces. To determine if the filling machine needs adjustment, each day the quality control manager measures the amount of soda per can for a random sample of 50 cans. Experience shows that its filling machines have a known population standard deviation of 0.35 ounces.

In today's sample of 50 cans of soda, the sample average amount of soda per can is 12.1 ounces. Construct and interpret a 90% confidence interval estimate for the true population average amount of

soda contained in all cans filled today at this bottling plant. Use a 90% confidence level.
X =

population parameter:  =

Random Variable X=

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 12.1

Population standard deviation =    = 0.35

Sample size = n = 50

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z_{0.05 = 1.645}

Margin of error = E = Z/2 * ( /n)

= 1.645 * ( 0.35 /  50 )

= 0.08

At 90% confidence interval estimate of the population mean is,

  ± E

12.1  ± 0.08   

( 12.02, 12.18 )  

We are 90% confidence that the true population average amount of soda contained in all cans filled today at this bottling plant between 12.02 and 12.18 ounces.