Question 1194260
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p = population proportion of people who prefer candidate A.


x = number of people who prefer candidate A
n = sample size


x = 481
n = 650
phat = best estimate of p
phat = sample proportion of people who prefer candidate A
phat = x/n
phat = 481/650
phat = 0.74
74% of the sample prefers candidate A.


At 95% confidence, the z critical value is roughly z = 1.960 which you use a reference table to determine.


E = margin of error
E = z*sqrt(phat*(1-phat)/n)
E = 1.960*sqrt(0.74*(1-0.74)/650)
E = 0.033721
This is approximate


L = lower boundary of the confidence interval
L = phat - E
L = 0.74 - 0.033721
L = 0.706279
L = 0.706


U = upper boundary of the confidence interval
U = phat + E
U = 0.74 + 0.033721
U = 0.773721
U = 0.774


The 95% confidence interval is roughly <font color=red>(0.706, 0.774)</font> which is of the format (L, U)


This is equivalent to writing 0.706 < p < 0.774 which is in the format L < p < U


We are 95% confident the population proportion (p) of people who prefer candidate A is between 0.706 and 0.774
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