Question

Suppose that 200 students are randomly selected from a local college campus to investigate the use of cell phones in classrooms. When asked if they are allowed to use cell phones in at least one of their classes, 40% of students responded yes. Using these results, with 95% confidence, the margin of error is 0.068 0.068 . How would the margin of error change if the sample size increased from 200 to 400 students? Assume that the proportion of students who say yes does not change significantly.

Answer 1

Solution :

Given that,

n = 400

x = 160 (40% of 400)

= x / n = 160 / 400 = 0.4

1 - = 1 - 0.4 = 0.6

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Margin of error = E = Z _{/ 2} * [ * (1 - ) / n]

= 1.96 * [(0.4 * .06) / 400]

= 0.048

The margin of error would change to 0.048