A preliminary sample of 1200 engineers has been taken, out

kungezwi8af

kungezwi8af

Answered question

2022-03-01

A preliminary sample of 1200 engineers has been taken, out of which 260 are females. The sample is used to estimate the proportion of female engineers denoted by pF .
Estimate the 95% confidence interval for pF.

Answer & Explanation

Vanesa Burrows

Vanesa Burrows

Beginner2022-03-02Added 2 answers

Step 1
There is a quick little approximation for CIs for sequences of bernoulli trials.
dnFn±z1α2dnMnFn
Here, z1α2 is the 1α2 quantile from the standard normal distribution, nF is the number of observed females, nM is the number of observed males, and n is the sum of both males and females.
So, doing some plugging and chugging yields.
d2601200±d1.961200d260(1200260)1200
So the CI is approximately [0.19, 0.24]
It may be worth noting that this estimate is called a Wald Interval and is known to be a bad estimate over all. Agresti-Coulli intervals for binomial proportions are better, but I doubt that is what your instructor is asking.

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