Question

The supervisor of a large engineering company wants to estimate the true proportion of workers wearing protective glasses on the job. At the current time a point estimate reveals that only 31.5 percent wear goggles. How big of a sample should be chosen in order to be 96% confident that the true proportion of workers wearing protective glasses is within a margin of error of 4%?

Answer 1

To estimate the required sample size, we can use the formula (Z^2 * p * (1-p)) / E^2. Plugging in the values, we find that a sample size of at least 481 workers should be chosen.

Step-by-step explanation:

To determine the sample size needed to estimate the true proportion of workers wearing protective glasses, we can use the formula:

n = (Z^2 * p * (1-p)) / E^2

Where:

• n is the sample size
• Z is the Z-value corresponding to the desired confidence level (for 96% confidence level, Z ≈ 1.75)
• p is the estimated proportion of workers wearing protective glasses (0.315 in this case)
• E is the margin of error (0.04 in this case)

Plugging in the values, we have:

n = (1.75^2 * 0.315 * (1-0.315)) / 0.04^2 ≈ 480.72

Therefore, a sample size of at least 481 workers should be chosen in order to be 96% confident that the true proportion of workers wearing protective glasses is within a margin of error of 4%.