FAQ: Simulating a Binomial Test - Confidence Intervals

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This community-built FAQ covers the “Confidence Intervals” exercise from the lesson “Simulating a Binomial Test”.

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This exercise can be found in the following Codecademy content:

Master Statistics with Python

FAQs on the exercise Confidence Intervals

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I’m confused on a concept here. Is the wording correct?
“We are 95% confident that, if each visitor has a 10% chance of making a purchase, a random sample of 500 visitors will make between 37 and 63 purchases.””

Our confidence interval that we use isn’t our ‘% confidence’ in our result is it? I mean, I know that sounds counter intuitive, but in this lesson we change the CI down to 90% and, our numbers changed as well as the accuracy. But from messing with the percentile range, it doesn’t appear there is as direct a correlation as this text implies. For example, extreme test of setting it to 40,60(20%- the middle quintile), and out of 20 runs, only 2 were not [48, 52](or 90% the same result).

So, what do we mean when we say we have 95% confidence or 90%?

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4

We can use the np.percentile() function to calculate this 95% interval as follows:

np.percentile(outcomes, [2.5,97.5])
# output: [37. 63.]

We calculated the 2.5th and 97.5th percentiles so that exactly 5% of the data falls outside those percentiles (2.5% above the 97.5th percentile, and 2.5% below the 2.5th percentile). This leaves us with a range covering 95% of the data.

Could you please help me understand this part? I don’t understand the reasoning in here at all!

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You want the middle 95% interval,
so there’s 5% left over (for being outside - meaning above and below the interval);
that’s 2.5% below the interval, and 2.5% above it (symmetry)
the cutoff for the lowest 2.5% is the 2.5th percentile,
the cutoff for the highest 2.5% is the 97.5th percentile (since 100 − 2.5 = 97.5)

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