Answer:
a
The 90% confidence interval that estimate the true proportion of students who receive financial aid is
b
Step-by-step explanation:
Considering question a
From the question we are told that
The sample size is n = 200
The number of student that receives financial aid is 
Generally the sample proportion is
=> 
=> 
From the question we are told the confidence level is 90% , hence the level of significance is
=> 
Generally from the normal distribution table the critical value of 
is
Generally the margin of error is mathematically represented as
=>
=> 
Generally 90% confidence interval is mathematically represented as
=>
Considering question b
From the question we are told that
The margin of error is E = 0.03
From the question we are told the confidence level is 99% , hence the level of significance is
=> 
Generally from the normal distribution table the critical value of is
Generally the sample size is mathematically represented as
![[\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p )](https://tex.z-dn.net/?f=%5B%5Cfrac%7BZ_%7B%5Cfrac%7B%5Calpha%20%7D%7B2%7D%20%7D%7D%7BE%7D%20%5D%5E2%20%2A%20%5C%5E%20p%20%281%20-%20%5C%5E%20p%20%29)
=> ![n = [\frac{2.58}{0.03} ]^2 * 0.59 (1 - 0.59 )](https://tex.z-dn.net/?f=n%20%3D%20%5B%5Cfrac%7B2.58%7D%7B0.03%7D%20%5D%5E2%20%2A%200.59%20%281%20-%200.59%20%29%20)
=>
