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In 2016, FiveThirtyEight conducted a poll with several questions about weddings. 34% of the 785 people...

In 2016, FiveThirtyEight conducted a poll with several questions about weddings. 34% of the 785 people surveyed who had not had a wedding said it was appropriate to ask for a plus one, while only 30% of the 265 people surveyed who had had a wedding said so. Construct a 90% confidence interval for the difference of these proportions (subtract the second proportion from the first).

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Answer #1

Here, , n1 = 265 , n2 = 785
p1cap = 0.3 , p2cap = 0.34


Standard Error, sigma(p1cap - p2cap),
SE = sqrt(p1cap * (1-p1cap)/n1 + p2cap * (1-p2cap)/n2)
SE = sqrt(0.3 * (1-0.3)/265 + 0.34*(1-0.34)/785)
SE = 0.0328

For 0.9 CI, z-value = 1.64
Confidence Interval,
CI = (p1cap - p2cap - z*SE, p1cap - p2cap + z*SE)
CI = (0.3 - 0.34 - 1.64*0.0328, 0.3 - 0.34 + 1.64*0.0328)
CI = (-0.0938 , 0.0138)

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