Question

a survey agency has asked students to speculate on whether hot dog is a sandwich or not. assume half of the survey participants believe that hot dog is a sandwich, while the other half believe it is not. how large a sample would the agency need to select to be 93% confident that the margin of error equals 0.05?

Answer 1

To be 93% confident with a margin of error of 0.05, the survey agency would need to select a sample size of approximately 330 students.

Step-by-step explanation:

To determine the sample size needed to estimate a population proportion with a desired level of confidence and margin of error, we can use the formula:

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

Where:

• n is the sample size
• Z is the Z-score corresponding to the desired level of confidence (in this case, for a 93% confidence level, Z = 1.8119)
• p is the estimated proportion (in this case, p = 0.5)
• E is the desired margin of error (in this case, E = 0.05)

Using these values in the formula, we get:

n = (1.8119^2 * 0.5 * (1-0.5)) / 0.05^2 = 329.2861

Therefore, to be 93% confident with a margin of error of 0.05, the survey agency would need to select a sample size of approximately 330 students.