Question

Office occupancy in a city is an indication of the economic health of the region in which it is located. A random sample of offices in two cities was selected, and the number of vacancies was recorded. The data are linked below. Construct a 95% confidence interval to estimate the difference in vacancy rates between these two cities. What conclusions can be made? Click the icon to view the occupancy data. The 95% confidence interval for the difference (p, - p2) is (Round to three decimal places as needed.) i Occupancy by City City 1 City 2 X1 23 X2 18 n1 175 n2 145 Print Done

Answer 1

Here, , n1 = 175 , n2 = 145
p1cap = 0.1314 , p2cap = 0.1241

Standard Error, sigma(p1cap - p2cap),
SE = sqrt(p1cap * (1-p1cap)/n1 + p2cap * (1-p2cap)/n2)
SE = sqrt(0.1314 * (1-0.1314)/175 + 0.1241*(1-0.1241)/145)
SE = 0.0374

For 0.95 CI, z-value = 1.96
Confidence Interval,
CI = (p1cap - p2cap - z*SE, p1cap - p2cap + z*SE)
CI = (0.1314 - 0.1241 - 1.96*0.0374, 0.1314 - 0.1241 + 1.96*0.0374)
CI = (-0.066 , 0.081)