# Properties of Sample Proportions

#### klsybrns

##### New Member
A city council is considering drafting legislation related to the exclusion of renters with children. Since implementation will be expensive, they will only consider proceeding if the true proportion of apartments that prohibit children is more than 75 percent. Suppose that out of 125 sampled appartments, 102 exclude renters with children.

a) What is the observed proportion of apartments which exclude renters with children ?
I have 0.816 for this, is this correct?

b) What is the true proportion of apartments which exclude renters with children ?
is this 0.75?

c) Compute the standard error of the observed proportion.

d) Find the 95 percent confidence interval for the true proportion of apartments which exclude renters with children.

e) Is the 99 percent confidence interval wider or narrower than the 95 percent confidence interval ?
I have that it is wider.

f) For the question above, test the hypothesis that the true proportion of apartments which exclude renters with children is greater than 75 percent.
- What is the null hypothesis ?

g) b) What is the alternative hypothesis ?
Is it p > 0.75?

h) Compute the value for the test statistic.

i) Compute the P-value.
Is this 0.04?

j) Would you reject the null hypothesis at significance level 0.01 ?

k) Suppose the test statistic in a similar study conducted elsewhere was found to be 4.21. Would you reject the null hypothesis at significance level 0.01 ?

#### trinker

##### ggplot2orBust
Hi! :welcome: We are glad that you posted here! This looks like a homework question though. Our homework help policy can be found here. We mainly just want to see what you have tried so far and that you have put some effort into the problem. I would also suggest checking out this thread for some guidelines on smart posting behavior that can help you get answers that are better much more quickly.