c) To estimate p with p unknown, E = 0.04, and 98% confidence

 

 

Since p is unknown and we need p to solve the above formula, we use p = 0.5 as this is commonly used in this situation but will result in the largest sample size.

 

p = 0.5

E = 0.04

z = 2.33 (from Table A.5 using 98/2 = 49 è 4900)

 

 

 

 

 

 

 

 

 

The sample size in this case is rounded up to 849.

 

d) To estimate p with E = 0.03, 95% confidence, and p thought to be approximately 0.70

 

E = 0.03

p = 0.70

z = 1.96 (from Table A.5 using 95/2 = 47.5 è 4750)

 

 

 

 

 

 

 

 

 

We will need a sample size rounded up to 897.