Question 1202947
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Answers:
<font color=red>0.608</font> < p < <font color=red>0.692</font>


p = 0.65 plusMinus <font color=red>0.042</font> 


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Work Shown:


phat = 325/500 = 0.65 = sample proportion
n = 500 = sample size


z = 1.960 at 95% confidence


E = margin of error
E = z*sqrt(phat*(1-phat)/n)
E = 1.960*sqrt(0.65*(1-0.65)/500)
E = 0.0418082288551
E = 0.042


L = lower boundary
L = phat - E
L = 0.65 - 0.042
L = 0.608


U = upper boundary
U = phat + E
U = 0.65 + 0.042
U = 0.692


The 95% confidence interval for p is roughly <font color=red>0.608</font> < p < <font color=red>0.692</font>
We can optionally condense that to the notation (0.608, 0.692); however, your teacher is opting for the more descriptive notation.


Yet another type of confidence interval notation would be to write p = 0.65 plusMinus <font color=red>0.042</font> where the 0.042 refers to the approximate margin of error.
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