Confidence Interval Coverage Binomial

A learning component illustrating coverage of confidence intervals for the mean of a binomial distribution.

Options

intro | (node|string): overrides default (interactive) intro text. Default: none.
quartileNotation | boolean: controls whether to use quartile notation in intro text. Default: true.
sampleStats | boolean: controls whether one should be able to switch between using the sample proportion or the known population success probability when calculating the standard error. Default: true.

Examples

Live Editor

<LearnConfidenceCoverageBinomial />

<LearnConfidenceCoverageBinomial />

Result

Confidence Interval Coverage for Sample Proportion

Now we will switch to asking a Yes/No question about a population. We are interested in estimating the true population proportion $p$ of "Yes" answers (for example, what proportion of the population has blue eyes?). We can take a sample of size $n$ , find how many observations in our sample are a "Yes" (X), and then estimate the true proportion $p$ with $\hat{p} = \frac{X}{n}$ . Then $\hat{p} \sim Normal (p, \sqrt{\frac{p (1 - p)}{n}})$ . Our confidence interval is then $\hat{p} \pm Z_{α / 2} \cdot \sqrt{\frac{p (1 - p)}{n}}$ $\hat{p} \pm Z_{α / 2} \cdot \sqrt{\frac{\hat{p} (1 - \hat{p})}{n}}$ .

For our choice of sample size (n), true proportion $p$ , and confidence level, we will simulate $20$ different samples from our normal distribution and calculate the corresponding sample proportions and confidence intervals.

Change parameters

Sample size (n):

True proportion (p):

Confidence level:
0.010.99

Confidence Intervals

Of the 20 confidence intervals, 19 capture the true proportion (coverage: 0.95).

Options​

Examples​

Confidence Interval Coverage for Sample Proportion

Change parameters

Confidence Intervals

Options

Examples