Question

A consumer advocate wants to collect a sample of jelly jars and measure the actual weight of the product in the container. He needs to collect enough data to construct a confidence interval with a margin of error of no more than 3 grams with 95​% confidence. The standard deviation of these jars is usually 3 grams. Estimate the minimum sample size required.

Answer 1

n=3.8416≅4

So Minimum Sample Size is 4

Explanation:

In order to find the minimum sample size, the formula we use will be:

`n= (Z^2*S^2)/(E^2)`

Where:

n is sample size

Z is the distribution

S is the standard deviation

E is the Margin of error

S=3 ,E=3

For Z:

Alpha=1-0.95=0.05

Alpha/2=0.025=2.5%

From Cumulative Standard Distribution Table:

Z at Alpha/2 = 1.960

`n= (1.960^2*3^2)/(3^2)`

n=3.8416≅4

So Minimum Sample Size is 4