Question

If we surveyed 30 smartphone users and found that 12 of them kept their smartphones for more than three years, calculate a 96% confidence interval for the proportion of all smartphone users who keep their smartphone for more than three years. the error term of the interval is ±

Answer 1

Sample Size = n = 30
Number of smartphone users = x = 12
Proportion of smartphone users = p = x/n = 12/30 = 0.4
Confidence interval = 96%
Z-value for confidence interval = 2.054

Error term of the interval is given by:


`E = z \sqrt{ (p(1-p))/(n) } \\ \\ E=2.054 \sqrt{ (0.4(0.6))/(30) } \\ \\ E=0.184`

The 96% confidence interval will be p ± E .
p - E = 0.4 - 0.184 = 0.216
p + E = 0.4 + 0.184 = 0.584

Therefore, the 96% confidence interval will be (0.216, 0.584)