AP Statistics Test B - Inference for Proportions - Part V Name __ 1. We have calculated a confidence interval based upon a sample of n=200 Now we want to get a better estimate with a margin of error only one fifth as large. We need a new sample with n at least __ A) 40 B) 240 C) 450 D) 1000 (E) 5000

## Step 1: Understand Margin of Error### The margin of error (MOE) is inversely proportional to the square root of the sample size , specifically .## Step 2: Calculate Margin of Error Reduction Factor### We aim to reduce the margin of error to one fifth of its original size: .## Step 3: Relate Sample Sizes for New Margin of Error### Using the relation , we derive: ## Step 4: Solve for the New Sample Size### Squaring both sides to isolate : Thus, .