Question

College officials want to estimate the percentage of students who carry a gun, knife, or other such weapon. How many randomly selected students must be surveyed in order to be 97% confident that the sample percentage has a margin of error of 1.5 percentage points? A) 743 B) 385 C) 168 D) 52

Answer 1

The number of randomly selected students that must be surveyed is 385.

Option (B) is true.

Explanation:

To determine the number of randomly selected students that must be surveyed, we can use the formula:

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

Where:

n = sample size

Z = Z-score corresponding to the desired confidence level (97% = 1.97)

p = estimated proportion (0.5, assuming maximum variability)

E = margin of error (0.015)

Plugging in the values, we get:

n = (1.97^2 * 0.5 * (1 - 0.5)) / 0.015^2

n ≈ 384.57

Since we cannot have a fraction of a student, we round up to the nearest whole number.

Therefore,

Option (B) is true.