Answer:
There is no enough evidence to claim that there is a difference between the two population proportions.
Step-by-step explanation:
We have to perform an hypothesis testing for a difference between two population proportions.
The null hypothesis will state that both proportions are the same, and the alternative hypothesis will state that they differ. This would be than a two-side hypothesis test.
We can write this as:
The significance level for this test is 0.05.
The sample of city residents with school-age children has a sample size n1=230 and a sample proportion p1=0.41
The sample of city residents without school-age children has a sample size n2=341 and a sample proportion p2=0.51
The weighted p, needed to calculate the standard error, is the weighted average of both sample proportions:
The standard error of the difference of proportions can now be calculated as:
The test statistic z is:
The P-value for this two side test and this value of the z-statistic is:
The P-value is bigger than the significance level, so the effect is not significant. The null hypothesis failed to be rejected.
There is no enough evidence to claim that there is a difference between the two population proportions.