Question

9) You are trying to determine if there is a difference between the proportion of residents of Atlanta who were born in Georgia and the proportion of the residents of Savannah who were born in Georgia. 500 residents out of 677 in Atlanta were born in Georgia, while 120 out of 157 Savannah residents were born in Georgia. Using a 2% level of significance, test the hypothesis that there is a difference between the two cities.

Answer 1

To test against

Here

The test statistic can be written as

which under H₀ follows a standard normal distribution.

We reject H₀ at 2% level of significance if P-value < 0.02

Now,

The value of the test statistic =

P-value =

Since P-value > 0.02, so we fail to reject H₀ at 2% level of significance and we can conclude that there is no difference between the proportion of residents of Atlanta who were born in Georgia and the proportion of the residents of Savannah who were born in Georgia.