An approximate 95% confidence interval for the true unemployment rate p is(p^−z2.5p^(1−p^)n,p^−z97.5p^(1−p^)n)=(0.079−1.960.079(1−0.079)4148,0.079+1.960.079(1−0.079)4148)=(0.071,0.087)What I'm mainly confused about is: how did they jump immediately to their first line?

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An approximate 95% confidence interval for the true unemployment rate p is(p^−z2.5p^(1−p^)n,p^−z97.5p^(1−p^)n)=(0.079−1.960.079(1−0.079)4148,0.079+1.960.079(1−0.079)4148)=(0.071,0.087)What I&#039;m mainly confused about is: how did they jump immediately to their first line?

RI5N6mv3 · Accepted Answer

Step 1It&#039;s a standard result that an approximate 100(1−α)% CI for a proportion p, obtained by observing x successes in a sequence of n independent Bernoulli trials each with success probability p is(p^−zp^(1−p^)n,p^+zp^(1−p^)n)where p^=xn is the estimate of p and z is the (1−α2) quantile of the standard normal distribution.So yes, assumptions have been made about independent Bernoulli trials.

An approximate \(\displaystyle{95}\%\) confidence interval for the

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