Question

A grocery store chain has been tracking data on the number of shoppers that use coupons. The data shows that 71% of all shoppers use coupons. 36 times out of 40 these results were considered accurate to within 3.5%. What is the margin of error?

a) 1.75%
b) 2.25%
c) 3.5%
d) 4.25%

Answer 1

The margin of error can be calculated using the standard error and critical value. In this case, the margin of error is 3.43%. Hence, closest option is c) 3.5%.

Step-by-step explanation:

The margin of error can be calculated using the formula:

Margin of Error = Critical value x Standard Error

Given that the data was accurate to within 3.5% in 36 out of 40 instances, we can calculate the standard error as:

Standard Error = Square root of (p(1-p)/n), where p is the proportion of shoppers using coupons and n is the sample size

Substituting the values into the formula, we have:

Standard Error = sqrt((0.71*(1-0.71))/40)

Using a z-score table, we find the critical value for a 95% confidence level is approximately 1.96

Therefore, the margin of error is:

Margin of Error = 1.96 x Standard Error = 1.96 x sqrt((0.71*(1-0.71))/40) = 0.0343

The margin of error is 3.43% (rounded to two decimal places).