Question

Barilla, a manufacturer of pasta has historical data that their packages of angel hair pasta have a known constant variance of 16 grams and average weight of 450 grams. However, their cardboard packaging often affects the total weight and a recent sample of 25 boxes found the average weight to be 430 grams. What is the margin of error for a 95% confidence interval to two decimal places?

Answer 1

Answer: 1.57

Explanation:

As we consider the given description, we have

n= 25

`\sigma^2=16\\\\\sigma=4`

Critical z-value for 95% confidence =
`z_(\alpha/2)=1.96`

The formula to find the margin of error :

`E=z_(\alpha/2)(\sigma)/(√(n))`

`E=(1.96)(4)/(√(25))\\\\=(1.96)(0.8)\\\\=1.568\approx1.57`

Hence, the margin of error for a 95% confidence interval =1.57