Question

The Nielsen Company surveyed 325 owners of Android phones and found that 196 of them planned to get another Android as their next phone. What is the lower bound for the 95% confidence interval for the proportion of Android users who plan to get another Android? Round to three decimal places (for example: 0.419). Write only a number as your answer.

Answer 1

Solution :

Given that,

n = 325

x = 196

= x / n = 196/ 325 = 0.603

1 - = 1 - 0. 603= 0.397

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

  = 0.05

Z = Z_0.05 = 1.645

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

= 1.645 * (((0.603 * 0.397) / 325) = 0.045

A 99 % confidence interval for population proportion p is ,

- E

0.603 - 0.045

0.558

lower bound = 0.558