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 99% confidence interval to estimate the difference in vacancy rates between these two cities. What conclusions can be made? city 1 city 2
x1=22 x2=14
n1=165 n2=140

We are confident at 99% that the difference between the two proportions is between . And since the confidence interval cotains the value 0 we don't have enough evidence to conclude that we have significant differences between the to proportions in these two cities

Step-by-step explanation:

represent the real population proportion for 1

represent the estimated proportion for 1

is the sample size required for 1

represent the real population proportion for 2

represent the estimated proportion for 2

is the sample size required for 2

represent the critical value for the margin of error  

The confidence interval for the difference of two proportions would be given by this formula  

For the 99% confidence interval the significance is and , and the critical value using the normal standard distribution.  

Replacing we got:

We are confident at 99% that the difference between the two proportions is between . And since the confidence interval cotains the value 0 we don't have enough evidence to conclude that we have significant differences between the to proportions in these two cities