Question

In a sample of 50 cases of juice, 3 had defects. The sampling method had a margin of error of 0.04.

What is the interval estimate for the proportion that would have defects in the form(lower limit, upper limit)?

Answer 1

Answer: To calculate the interval estimate for the proportion of defects in the juice samples, we'll use the formula for the confidence interval for a proportion.

Confidence Interval = Sample Proportion ± Margin of Error

Given information:

Sample size (n) = 50 cases

Number of defects (x) = 3 cases

Margin of Error = 0.04

Step 1: Calculate the sample proportion (p-hat):

Sample Proportion (p-hat) = Number of defects / Sample size

p-hat = 3 / 50 = 0.06

Step 2: Calculate the lower and upper limits of the confidence interval:

Lower Limit = p-hat - Margin of Error

Upper Limit = p-hat + Margin of Error

Lower Limit = 0.06 - 0.04 = 0.02

Upper Limit = 0.06 + 0.04 = 0.10

So, the interval estimate for the proportion of defects in the juice samples is (0.02, 0.10). This means we are 95% confident that the true proportion of defects in the population lies within this interval.