Interactive: confidence-interval coverage

import numpy as np
import plotly.graph_objects as go
from IPython.display import HTML

# Okabe-Ito colorblind-safe palette
OI_BLUE      = "#0072B2"   # intervals that CAPTURE the true mean  (circle marker)
OI_VERMILION = "#D55E00"   # intervals that MISS the true mean     (x marker)
OI_GREEN     = "#009E73"   # the true-mean reference line

# An invented "true" population. SIMULATED data, fixed seed -> identical every
# build. No real dataset value is claimed: mu and sigma are round teaching
# numbers in arbitrary units, NOT a measured Kern County statistic.
TRUE_MU, SIGMA, N, CONF = 50.0, 12.0, 30, 0.95

# 95% normal critical value. scipy is unavailable in the build venv, so we use
# the exact constant z* = norm.ppf(0.975) (agrees to 9 decimals). For known
# sigma the CI half-width z*-sigma/sqrt(n) is the same for every sample, which
# is why some intervals shift off-center enough to miss mu.
Z = 1.959963984540054

rng = np.random.default_rng(2200)
n_batches, m = 20, 20            # 20 batches; 20 fresh 95% CIs drawn per batch

half = Z * SIGMA / np.sqrt(N)    # CI half-width (margin of error), known-sigma

frames, lo_global, hi_global = [], np.inf, -np.inf
for b in range(n_batches):
    xbars = rng.normal(TRUE_MU, SIGMA / np.sqrt(N), size=m)   # sample means
    los, his = xbars - half, xbars + half
    covers = (los <= TRUE_MU) & (TRUE_MU <= his)             # did the CI catch mu?
    n_cap = int(covers.sum())

    colors = np.where(covers, OI_BLUE, OI_VERMILION)
    syms   = np.where(covers, "circle", "x")                 # shape, not color-alone
    lo_global = min(lo_global, los.min())
    hi_global = max(hi_global, his.max())

    frames.append(go.Frame(
        name=str(b),
        data=[go.Scatter(
            x=xbars, y=list(range(m)), mode="markers",
            marker=dict(color=list(colors), symbol=list(syms), size=9,
                        line=dict(width=1, color="white")),
            error_x=dict(type="data", array=[half] * m, color="#999999",
                         thickness=1.4, width=0),
            hovertemplate="CI: %{x:.1f} &#177; " + f"{half:.1f}<extra></extra>",
        )],
        layout=go.Layout(title=dict(text=(
            "Confidence-interval coverage (simulated): vermillion &#10005; "
            "intervals miss the true mean<br>"
            f"<sup>Batch {b + 1} of {n_batches}: {n_cap} of {m} 95% intervals "
            "captured &#956; (green dashed line)</sup>"))),
    ))

pad = 0.06 * (hi_global - lo_global)
fig = go.Figure(
    data=frames[0].data,
    frames=frames,
    layout=go.Layout(
        template="simple_white",
        xaxis_title="95% confidence interval for the mean (simulated units)",
        yaxis_title="interval number (1 to 20)",
        xaxis_range=[lo_global - pad, hi_global + pad],   # FIXED so frames align
        height=540, margin=dict(t=90, r=20, b=60, l=70), showlegend=False,
        shapes=[dict(type="line", x0=TRUE_MU, x1=TRUE_MU, y0=-1, y1=m,
                     line=dict(color=OI_GREEN, dash="dash", width=2))],
        annotations=[dict(x=TRUE_MU, y=m - 0.5, xanchor="left", yanchor="bottom",
                          text="  true mean &#956;", showarrow=False,
                          font=dict(color=OI_GREEN))],
        title=dict(text=(
            "Confidence-interval coverage (simulated): vermillion &#10005; "
            "intervals miss the true mean<br>"
            f"<sup>Press Play: each batch draws 20 fresh 95% intervals; about "
            "95% capture &#956; (green dashed line)</sup>")),
        updatemenus=[dict(type="buttons", x=0.0, y=1.16, xanchor="left",
            showactive=False, buttons=[
                dict(label="&#9654; Play", method="animate",
                     args=[None, {"frame": {"duration": 900, "redraw": True},
                                  "fromcurrent": True,
                                  "transition": {"duration": 0}}]),
                dict(label="&#10073;&#10073; Pause", method="animate",
                     args=[[None], {"frame": {"duration": 0, "redraw": False},
                                    "mode": "immediate"}])])],
        sliders=[dict(active=0, pad={"t": 45},
            currentvalue={"prefix": "Batch "},
            steps=[dict(method="animate", label=str(b + 1),
                        args=[[str(b)], {"mode": "immediate",
                                         "frame": {"duration": 0, "redraw": True},
                                         "transition": {"duration": 0}}])
                   for b in range(n_batches)])],
    ),
)

# THE GOTCHA FIX: emit text/html ourselves (embeddable div + CDN plotly.js).
HTML(fig.to_html(full_html=False, include_plotlyjs="cdn"))