Question

ATT wants to determine the current percentage of customers aged 50+ who use text messaging on their iPhones. How many customers aged 50+ should the company survey in order to be 90% confident that the estimated (sample) proportion is within three percentage points of the true population proportion of customers aged 50+ who use text messaging on their cell phones.

Answer 1

Solution:

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 3% = 0.03

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z/2 = Z0.05 = 1.645

Sample size = n = ((Z / 2) / E)2 * * (1 - )

= (1.645/ 0.03)2 * 0.5 * 0.5

= 751.54

= 752

n = sample size = 752