Question

A study of two hundred teens found that the number of hours they spend on social networking sites each week is normally distributed with a mean of 12 hours. the population standard deviation is 4 hours. what is the margin of error for a 98% confidence interval?

Answer 1

The confidence interval formula is as follows :

C.I = X + /​- (α/√n) Zβ/2

The β = 1 - 0.98 = 0.02

0.02/2 = 0.01

Z0. 01 = 2.57

α = 4

n = 200

X = 12

√200 = 14.14

Doing the substitution :

α / √n = 4/14.14 = 0.2829

0.2829 × 2.57 = 0.7271

The interval is :

Lower limit : 12 - 0.7271 = 11.2729

Upper limit : 12 + 0.7271 = 12.7271