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 5 grams grams with 99​% confidence. The standard deviation of these jars is usually 4 grams. Estimate the minimum sample size required.

The minimum sample size required is how many jars? ​(Round up to the nearest whole​ number.)

Answer 1

Solution :

Given that,

standard deviation = = 4

margin of error = E = 5

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

Sample size = n = ((Z_/2 * ) / E)²

= ((2.576 * 4) / 5)²

= 4.24

= 4

Sample size = 4