Question 1171865
<font color=black size=3>
Part (a)
The best estimate for the population proportion p is the sample proportion phat (read as "p-hat")


In this case, 
phat = (number of yes responses)/(number total)
phat = x/n
phat = 579/943
phat = 0.61399787910922
phat = 0.614
Which is approximate.


====================================================
Part (b)


At 99% confidence, the z critical value is roughly z = 2.576


The margin of error is
E = z*sqrt(phat*(1-phat)/n)
E = 2.576*sqrt(0.61399787910922*(1-0.61399787910922)/943)
E = 0.040838360004
E = 0.04
This is approximate. 


====================================================
Part (c)


We'll use the results of parts (a) and (b)


The lower boundary L of the confidence interval is 
L = (center) - (margin of error)
L = (phat) - (E)
L = 0.61399787910922 - 0.040838360004
L = 0.57315951910522
L = 0.5732


And the upper boundary U is
L = (center) + (margin of error)
L = (phat) + (E)
L = 0.61399787910922 + 0.040838360004
L = 0.65483623911322
L = 0.6548


The 99% confidence interval in the form L < p < U is roughly 0.5732 < p < 0.6548


We can write this as (0.5732, 0.6548)


We are 99% confident that the population proportion p is between 0.5732 and 0.6548
</font>