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. How would the margin of error change if the sample size increased from 200 to 400 students?

It would change to 0.04802

Step-by-step explanation:

from this question we have that n became 400

40% of 400

= 160

p* = 160/400

= 0.4

1 - p* =

= 1 - 0.4

= 0.6

at confidence level,

1 - 0.95

= 0.05

alpha/2 = 0.025

z= 1.96

margin of error. E

= 1.96 x √[(0.4 x 0.6)/400]

= 1.96 x 0.0245

= 0.04802

M.E = 0.04802

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west

jbankston is right, use thhe link and you should find the answer.