Question 1204140
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phat = sample proportion = 0.316
phat's job is to estimate the population proportion p


n = sample size = 95


At 90% confidence, the z critical value is approximately z = 1.645
This is something to memorize.
Alternatively you can use a Z table or stats calculator (such as a TI83).


Then,
E = margin of error for a proportion
E = z*sqrt(phat*(1-phat)/n)
E = 1.645*sqrt(0.316*(1-0.316)/95)
E = 0.07846494809787
E = 0.078465 approximately


Afterward we compute the lower and upper bounds (L and U)
L = lower boundary
L = phat - E
L = 0.316 - 0.078465
L = 0.237535
L = 0.238


U = upper boundary
U = phat + E
U = 0.316 + 0.078465
U = 0.394465
U = 0.394


The 90% confidence interval in the format L < p < U would be <font color=red size=4>approximately 0.238 < p < 0.394</font>
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