Question

A random sample of 500 customers was selected to estimate the proportion of customers that purchase produce on a regular basis. What is the maximum margin of error if a 90% confidence interval is constructed?

A) 2%
B) 3%
C) 4%
D) 5%

Answer 1

The maximum margin of error for a 90% confidence interval is C) 4%.

Step-by-step explanation:

To calculate the maximum margin of error for a confidence interval, we need to use the formula:

Margin of Error = Z * sqrt((p * (1 - p))/n)

Where:

• Z is the Z-score associated with the desired confidence level (in this case, 90% confidence level corresponds to a Z-score of approximately 1.645)
• p is the estimated proportion (we don't have this information)
• n is the sample size (we have 500)

Since we don't have the estimated proportion, we need to use the worst case scenario (p = 0.5) to get the maximum margin of error.

Plugging the values into the formula, we have:

Margin of Error = 1.645 * sqrt((0.5 * (1 - 0.5))/500) = 0.0347 (rounded to 4%)

The maximum margin of error for a 90% confidence interval is 4%, so the correct answer is C) 4%.