Question

Suppose that you are interested in estimating the mean amount of soda that is placed in 2-liter bottles at the local bottling plant of a large nationally known soda company. The bottling plant has informed the inspection division that the standard deviation for 2-liter bottles is .07 liter. A random sample of fifty 2-liter bottles obtained from this bottling plant indicated a sample mean of 2.02 liters.

a. What is the point estimate of the population mean?

b. Calculate the 95% margin of error for your point estimate in part (a).

c. How large a sample would you need to make the margin of error 1/3 as large as it is in (b)?

Answer 1

Ans:

a)Point estimate of mean=2.02

b)

Margin of error=1.96*(0.07/sqrt(50))=0.0194

c)

As,margin of error is inversely proportional to sqrt(n),so to make the margin of error one-third,increase the sample size 9 times.

so,if sample size =9*50=450

margin of error=1.96*(0.07/sqrt(450))=0.006468 i.e. 1/3 of part b