Styled UI: cleaner cards, compact layout, embed-ready

src/streamlit_app.py

@@ -1,5 +1,5 @@
 # mean_inference_app.py
-# Streamlit ≥1.32
+# Streamlit ≥1.32 — Styled for embedding
 
 import streamlit as st
 import pandas as pd
@@ -7,268 +7,323 @@ import numpy as np
 from scipy.stats import norm, t
 import io
 
-# ---------- Page ----------
-st.title("Inference for Means (Continous Variables): Confidence Interval & Hypothesis Test")
-
-st.markdown(r"""
-This app performs inference on population means:
-
-1. **One-Sample Mean**
-2. **Difference Between Two Independent Means**
+# ---------- Page Config ----------
+st.set_page_config(
+    page_title="Inference for Means",
+    page_icon="📈",
+    layout="centered",
+    initial_sidebar_state="collapsed"
+)
 
-For either case you may construct a **confidence interval** or run a **hypothesis test**,
-choosing a *z* (large-sample approximation) or *t* (σ unknown; normal population) approach.
-""")
+# ---------- Custom CSS for Clean Embed Look ----------
+st.markdown("""
+<style>
+    /* Compact header */
+    .main h1 { font-size: 1.6rem; margin-bottom: 0.5rem; }
+    
+    /* Tighter spacing */
+    .block-container { padding-top: 1.5rem; padding-bottom: 1rem; }
+    
+    /* Styled result cards */
+    .result-card {
+        background: linear-gradient(135deg, #667eea 0%, #764ba2 100%);
+        padding: 1.2rem;
+        border-radius: 10px;
+        color: white;
+        text-align: center;
+        margin: 0.5rem 0;
+    }
+    .result-card h3 {
+        margin: 0;
+        font-size: 0.85rem;
+        font-weight: 400;
+        opacity: 0.9;
+    }
+    .result-card p {
+        margin: 0.3rem 0 0 0;
+        font-size: 1.5rem;
+        font-weight: 600;
+    }
+    
+    /* CI card */
+    .ci-card { background: linear-gradient(135deg, #11998e 0%, #38ef7d 100%); }
+    
+    /* Reject card */
+    .reject-card { background: linear-gradient(135deg, #eb3349 0%, #f45c43 100%); }
+    
+    /* Fail to reject card */
+    .accept-card { background: linear-gradient(135deg, #56ab2f 0%, #a8e063 100%); }
+    
+    /* Compact inputs */
+    .stNumberInput > div > div > input { padding: 0.4rem; }
+    
+    /* Subtle divider */
+    hr { margin: 1rem 0; border: none; border-top: 1px solid #e0e0e0; }
+    
+    /* Info boxes */
+    .info-box {
+        background: #f8f9fa;
+        border-left: 3px solid #667eea;
+        padding: 0.7rem 1rem;
+        border-radius: 0 8px 8px 0;
+        margin: 0.5rem 0;
+        font-size: 0.9rem;
+    }
+    
+    /* Hide Streamlit branding for cleaner embed */
+    #MainMenu {visibility: hidden;}
+    footer {visibility: hidden;}
+    header {visibility: hidden;}
+</style>
+""", unsafe_allow_html=True)
+
+# ---------- Title ----------
+st.markdown("## 📈 Inference for Means")
+st.caption("Confidence intervals & hypothesis tests for one or two means")
 
 # ---------- INPUTS ----------
-st.header("Inputs")
-
-# Inference type (one- vs two-sample)
-inf_type = st.radio(
-    "Choose inference:",
-    ["One-Sample Mean", "Two-Sample Mean (independent)"],
-    key="inf_type"
-)
+with st.container():
+    col1, col2 = st.columns(2)
+    with col1:
+        inf_type = st.radio("Inference type:", ["One-Sample", "Two-Sample"],
+                           key="inf_type", horizontal=True)
+    with col2:
+        analysis_type = st.radio("Analysis:", ["Confidence Interval", "Hypothesis Test"],
+                                key="analysis_type", horizontal=True)
 
-# Analysis type
-analysis_type = st.radio(
-    "Choose analysis:",
-    ["Confidence Interval", "Hypothesis Test"],
-    key="analysis_type"
-)
+st.markdown("<hr>", unsafe_allow_html=True)
 
 # Distribution choice
 dist_choice = st.radio(
     "Sampling distribution:",
-    ["Large sample Approximation → *z*", "Small sample (σ unknown and normal population) → *t*"],
-    key="dist_choice"
+    ["z (large sample)", "t (small sample, σ unknown)"],
+    key="dist_choice",
+    horizontal=True
 )
+dist_is_z = dist_choice.startswith("z")
+
+st.markdown("<hr>", unsafe_allow_html=True)
 
 # ---------- Sample Data Inputs ----------
-if inf_type == "One-Sample Mean":
-    st.subheader("Sample")
-    n = st.number_input("Sample size (n)", min_value=2, step=1, value=30, key="n")
-    xbar = st.number_input("Sample mean (x̄)", format="%.4f", value=0.0, key="xbar")
-    s = st.number_input("Sample standard deviation (s)  •  use σ if known", min_value=0.0001,
-                        format="%.4f", value=1.0, key="s")
-else:
+if inf_type == "One-Sample":
+    cols = st.columns(3)
+    with cols[0]:
+        n = st.number_input("n", min_value=2, step=1, value=30, key="n")
+    with cols[1]:
+        xbar = st.number_input("x̄", format="%.4f", value=0.0, key="xbar")
+    with cols[2]:
+        s = st.number_input("s (or σ)", min_value=0.0001, format="%.4f", value=1.0, key="s")
+    
+    st.markdown(f'<div class="info-box">SE = s/√n = <strong>{s/np.sqrt(n):.4f}</strong></div>', 
+                unsafe_allow_html=True)
+
+else:  # Two-Sample
     col1, col2 = st.columns(2)
     with col1:
-        st.subheader("Group 1")
-        n1 = st.number_input("Sample size n₁", min_value=2, step=1, value=30, key="n1")
-        xbar1 = st.number_input("Sample mean x̄₁", format="%.4f", value=0.0, key="xbar1")
-        s1 = st.number_input("Sample standard deviation s₁", min_value=0.0001,
-                             format="%.4f", value=1.0, key="s1")
+        st.markdown("**Group 1**")
+        c1, c2, c3 = st.columns(3)
+        with c1:
+            n1 = st.number_input("n₁", min_value=2, step=1, value=30, key="n1")
+        with c2:
+            xbar1 = st.number_input("x̄₁", format="%.4f", value=0.0, key="xbar1")
+        with c3:
+            s1 = st.number_input("s₁", min_value=0.0001, format="%.4f", value=1.0, key="s1")
+    
     with col2:
-        st.subheader("Group 2")
-        n2 = st.number_input("Sample size n₂", min_value=2, step=1, value=30, key="n2")
-        xbar2 = st.number_input("Sample mean x̄₂", format="%.4f", value=0.0, key="xbar2")
-        s2 = st.number_input("Sample standard deviation s₂", min_value=0.0001,
-                             format="%.4f", value=1.0, key="s2")
+        st.markdown("**Group 2**")
+        c1, c2, c3 = st.columns(3)
+        with c1:
+            n2 = st.number_input("n₂", min_value=2, step=1, value=30, key="n2")
+        with c2:
+            xbar2 = st.number_input("x̄₂", format="%.4f", value=0.0, key="xbar2")
+        with c3:
+            s2 = st.number_input("s₂", min_value=0.0001, format="%.4f", value=1.0, key="s2")
+
+st.markdown("<hr>", unsafe_allow_html=True)
 
 # ---------- CI / HT specific controls ----------
 if analysis_type == "Confidence Interval":
-    conf_level = st.slider("Confidence level", 0.80, 0.99, 0.95, step=0.01,
-                           key="conf_level")
-else:  # Hypothesis Test
-    alpha = st.slider("Significance level (α)", 0.01, 0.10, 0.05, step=0.01, key="alpha")
-    if inf_type == "One-Sample Mean":
-        mu0 = st.number_input("Null mean (μ₀)", format="%.4f", value=0.0, key="mu0")
-        alt = st.radio("Alternative hypothesis (H₁):",
-                       ["μ ≠ μ₀ (Two-sided)",
-                        "μ > μ₀ (Right-sided)",
-                        "μ < μ₀ (Left-sided)"],
-                       key="alt_one")
-    else:
-        alt = st.radio("Alternative hypothesis (H₁):",
-                       ["μ₁ ≠ μ₂ (Two-sided)",
-                        "μ₁ > μ₂ (Right-sided)",
-                        "μ₁ < μ₂ (Left-sided)"],
-                       key="alt_two")
-
-# ---------- RUN ----------
-run = st.button("Run Analysis")
-
-st.header("Results")
-
-# ===== ONE-SAMPLE =====
-if run and inf_type == "One-Sample Mean" and n >= 2:
-    se = s / np.sqrt(n)
-    df = n - 1
-    dist_is_z = dist_choice.startswith("Large")
-
-    if analysis_type == "Confidence Interval":
-        # critical value
-        if dist_is_z:
-            crit = norm.ppf(1 - (1 - conf_level) / 2)
-        else:
-            crit = t.ppf(1 - (1 - conf_level) / 2, df)
-        margin = crit * se
-        lower, upper = xbar - margin, xbar + margin
-
-        # --- Display ---
-        st.subheader("Confidence Interval")
-        st.metric("Sample mean (x̄)", f"{xbar:.4f}")
-        st.metric(f"{conf_level*100:.1f}% CI",
-                  f"[{lower:.4f}, {upper:.4f}]")
-        st.write(f"Standard Error: **{se:.4f}**")
-        st.write(f"Critical value ({'z' if dist_is_z else 't'}): **{crit:.4f}**")
-        st.write(f"Margin of Error: **{margin:.4f}**")
-
-        results = {
-            "Analysis": ["CI – One-Sample"],
-            "n": [n], "x̄": [xbar], "s": [s],
-            "SE": [se], "Dist": ["z" if dist_is_z else "t"],
-            "Conf Level": [conf_level],
-            "Lower": [lower], "Upper": [upper]
-        }
-
-    else:  # Hypothesis Test
-        if dist_is_z:
-            zt = (xbar - mu0) / se
-            p_val = (2 if "≠" in alt else 1) * \
-                    (1 - norm.cdf(abs(zt))) if "≠" in alt else \
-                    (1 - norm.cdf(zt) if ">" in alt else norm.cdf(zt))
-            crit = norm.ppf(1 - alpha/2) if "≠" in alt else norm.ppf(1 - alpha)
-        else:
-            zt = (xbar - mu0) / se  # same formula, but follows t-df
-            p_val = (2 if "≠" in alt else 1) * \
-                    (1 - t.cdf(abs(zt), df)) if "≠" in alt else \
-                    (1 - t.cdf(zt, df) if ">" in alt else t.cdf(zt, df))
-            crit = t.ppf(1 - alpha/2, df) if "≠" in alt else t.ppf(1 - alpha, df)
-
-        decision = ("Reject H₀", "Fail to reject H₀")[p_val > alpha]
-
-        # --- Display ---
-        st.subheader("Hypothesis Test")
-        st.metric(f"{'z' if dist_is_z else 't'}-statistic", f"{zt:.4f}")
-        st.metric("p-value", f"{p_val:.4g}")
-        st.write(f"Standard Error: **{se:.4f}**")
-        st.write(f"α = {alpha:.2f}  •  Alternative: **{alt}**")
-        st.write(f"Critical value(s): **{('±' if '≠' in alt else '')}{crit:.4f}**")
-        st.subheader("Conclusion")
-        if decision == "Reject H₀":
-            st.success(f"Reject H₀ at α = {alpha:.2f}.")
-        else:
-            st.info(f"Fail to reject H₀ at α = {alpha:.2f}.")
-
-        results = {
-            "Analysis": ["HT – One-Sample"],
-            "n": [n], "x̄": [xbar], "s": [s], "μ₀": [mu0],
-            "SE": [se], "Dist": ["z" if dist_is_z else "t"],
-            "α": [alpha], "Alt": [alt],
-            "Stat": [zt], "p": [p_val],
-            "Reject_H0": [decision.startswith("Reject")]
-        }
-
-# ===== TWO-SAMPLE =====
-elif run and inf_type.startswith("Two-Sample") and n1 >= 2 and n2 >= 2:
-    se = np.sqrt(s1**2/n1 + s2**2/n2)
-    df_num = (s1**2/n1 + s2**2/n2)**2
-    df_den = (s1**2/n1)**2/(n1-1) + (s2**2/n2)**2/(n2-1)
-    df = df_num / df_den
-    diff = xbar1 - xbar2
-    dist_is_z = dist_choice.startswith("Large")
-
-    if analysis_type == "Confidence Interval":
-        crit = norm.ppf(1 - (1 - conf_level) / 2) if dist_is_z else t.ppf(
-            1 - (1 - conf_level) / 2, df)
-        margin = crit * se
-        lower, upper = diff - margin, diff + margin
-
-        st.subheader("Confidence Interval")
-        st.metric("Difference (x̄₁ − x̄₂)", f"{diff:.4f}")
-        st.metric(f"{conf_level*100:.1f}% CI",
-                  f"[{lower:.4f}, {upper:.4f}]")
-        st.write(f"Standard Error: **{se:.4f}**")
-        st.write(f"df (Welch): **{df:.1f}**")
-        st.write(f"Critical value ({'z' if dist_is_z else 't'}): **{crit:.4f}**")
-
-        results = {
-            "Analysis": ["CI – Two-Sample"],
-            "n₁": [n1], "x̄₁": [xbar1], "s₁": [s1],
-            "n₂": [n2], "x̄₂": [xbar2], "s₂": [s2],
-            "SE": [se], "df": [df],
-            "Dist": ["z" if dist_is_z else "t"],
-            "Conf Level": [conf_level],
-            "Lower": [lower], "Upper": [upper]
-        }
-
-    else:  # Hypothesis Test
-        zt = diff / se
-        if dist_is_z:
-            p_val = (2 if "≠" in alt else 1) * \
-                    (1 - norm.cdf(abs(zt))) if "≠" in alt else \
-                    (1 - norm.cdf(zt) if ">" in alt else norm.cdf(zt))
-            crit = norm.ppf(1 - alpha/2) if "≠" in alt else norm.ppf(1 - alpha)
-        else:
-            p_val = (2 if "≠" in alt else 1) * \
-                    (1 - t.cdf(abs(zt), df)) if "≠" in alt else \
-                    (1 - t.cdf(zt, df) if ">" in alt else t.cdf(zt, df))
-            crit = t.ppf(1 - alpha/2, df) if "≠" in alt else t.ppf(1 - alpha, df)
-
-        decision = ("Reject H₀", "Fail to reject H₀")[p_val > alpha]
-
-        st.subheader("Hypothesis Test")
-        st.metric(f"{'z' if dist_is_z else 't'}-statistic", f"{zt:.4f}")
-        st.metric("p-value", f"{p_val:.4g}")
-        st.write(f"Standard Error: **{se:.4f}**")
-        st.write(f"df (Welch): **{df:.1f}**")
-        st.write(f"α = {alpha:.2f}  •  Alternative: **{alt}**")
-        st.write(f"Critical value(s): **{('±' if '≠' in alt else '')}{crit:.4f}**")
-        st.subheader("Conclusion")
-        if decision == "Reject H₀":
-            st.success(f"Reject H₀ at α = {alpha:.2f}.")
+    conf_level = st.select_slider("Confidence level:",
+                                  options=[0.90, 0.95, 0.99], value=0.95,
+                                  format_func=lambda x: f"{x*100:.0f}%", key="conf_level")
+else:
+    cols = st.columns([1, 2])
+    with cols[0]:
+        alpha = st.select_slider("α level:", options=[0.01, 0.05, 0.10], value=0.05, key="alpha")
+    with cols[1]:
+        if inf_type == "One-Sample":
+            mu0 = st.number_input("Null mean (μ₀):", format="%.4f", value=0.0, key="mu0")
+            alt = st.radio("H₁:", ["μ ≠ μ₀", "μ > μ₀", "μ < μ₀"], horizontal=True, key="alt_one")
         else:
-            st.info(f"Fail to reject H₀ at α = {alpha:.2f}.")
-
-        results = {
-            "Analysis": ["HT – Two-Sample"],
-            "n₁": [n1], "x̄₁": [xbar1], "s₁": [s1],
-            "n₂": [n2], "x̄₂": [xbar2], "s₂": [s2],
-            "SE": [se], "df": [df],
-            "Dist": ["z" if dist_is_z else "t"],
-            "α": [alpha], "Alt": [alt],
-            "Stat": [zt], "p": [p_val],
-            "Reject_H0": [decision.startswith("Reject")]
-        }
+            alt = st.radio("H₁:", ["μ₁ ≠ μ₂", "μ₁ > μ₂", "μ₁ < μ₂"], horizontal=True, key="alt_two")
 
-# Warn if inputs invalid
-elif run:
-    st.warning("Please ensure sample sizes are ≥ 2 and standard deviations are > 0.")
-
-# ---------- DOWNLOAD ----------
-if run and 'results' in locals():
-    df_out = pd.DataFrame(results)
-    buff = io.BytesIO()
-    with pd.ExcelWriter(buff, engine="xlsxwriter") as writer:
-        df_out.to_excel(writer, index=False, sheet_name="Summary")
-    st.download_button(
-        label="Download Summary (.xlsx)",
-        data=buff.getvalue(),
-        file_name=f"mean_inference_{analysis_type.lower().replace(' ', '_')}.xlsx",
-        mime="application/vnd.openxmlformats-officedocument.spreadsheetml.sheet"
-    )
-
-# ---------- THEORETICAL NOTES ----------
-st.header("Theoretical Notes")
-
-st.markdown(r"""
-### One-Sample Mean
-* **Assumptions:** simple random sample; normal population *or* large $n$.
-* **Standard error:** $SE = \dfrac{s}{\sqrt{n}}$
-* **Confidence interval:**  
-  $ \displaystyle \bar x \;\pm\; z_{1-\alpha/2} \,SE $  *(or)*  
-  $ \displaystyle \bar x \;\pm\; t_{1-\alpha/2,\;df=n-1}\,SE $
-* **Test statistic:**  
-  $ \displaystyle z = \frac{\bar x-\mu_0}{SE} $   *(or)*  
-  $ \displaystyle t_{df} = \frac{\bar x-\mu_0}{SE} $
-
-### Two Independent Means
-* **Standard error (Welch):**  
-  $ \displaystyle SE = \sqrt{\frac{s_1^{2}}{n_1}+\frac{s_2^{2}}{n_2}} $
-* **df (Welch–Satterthwaite):**  
-  $ \displaystyle
-      df = \frac{(s_1^{2}/n_1 + s_2^{2}/n_2)^2}
-                 {(s_1^{2}/n_1)^2/(n_1-1) + (s_2^{2}/n_2)^2/(n_2-1)} $
+# ---------- RUN ----------
+run = st.button("▶ Calculate", type="primary", use_container_width=True)
+
+# ---------- Helper function ----------
+def result_card(label, value, card_class="result-card"):
+    return f'<div class="{card_class}"><h3>{label}</h3><p>{value}</p></div>'
+
+# ===== RESULTS =====
+if run:
+    st.markdown("<hr>", unsafe_allow_html=True)
+    
+    # ===== ONE-SAMPLE =====
+    if inf_type == "One-Sample" and n >= 2:
+        se = s / np.sqrt(n)
+        df = n - 1
+        
+        if analysis_type == "Confidence Interval":
+            crit = norm.ppf(1 - (1 - conf_level)/2) if dist_is_z else t.ppf(1 - (1 - conf_level)/2, df)
+            margin = crit * se
+            lower, upper = xbar - margin, xbar + margin
+            
+            cols = st.columns(2)
+            with cols[0]:
+                st.markdown(result_card("Sample Mean (x̄)", f"{xbar:.4f}"), unsafe_allow_html=True)
+            with cols[1]:
+                st.markdown(result_card(f"{conf_level*100:.0f}% Confidence Interval", 
+                                       f"[{lower:.4f}, {upper:.4f}]", "result-card ci-card"), unsafe_allow_html=True)
+            
+            with st.expander("📋 Details", expanded=False):
+                st.write(f"**Standard Error:** {se:.4f}")
+                st.write(f"**Critical value ({'z' if dist_is_z else f't(df={df})'}):** ±{crit:.4f}")
+                st.write(f"**Margin of Error:** {margin:.4f}")
+            
+            results = {"Analysis": ["CI"], "n": [n], "x̄": [xbar], "s": [s],
+                      "SE": [se], "Lower": [lower], "Upper": [upper]}
+
+        else:  # Hypothesis Test
+            stat = (xbar - mu0) / se
+            
+            if "≠" in alt:
+                p_val = 2 * (1 - (norm.cdf(abs(stat)) if dist_is_z else t.cdf(abs(stat), df)))
+                crit = norm.ppf(1 - alpha/2) if dist_is_z else t.ppf(1 - alpha/2, df)
+            elif ">" in alt:
+                p_val = 1 - (norm.cdf(stat) if dist_is_z else t.cdf(stat, df))
+                crit = norm.ppf(1 - alpha) if dist_is_z else t.ppf(1 - alpha, df)
+            else:
+                p_val = norm.cdf(stat) if dist_is_z else t.cdf(stat, df)
+                crit = -(norm.ppf(1 - alpha) if dist_is_z else t.ppf(1 - alpha, df))
+
+            reject = p_val <= alpha
+            
+            cols = st.columns(2)
+            with cols[0]:
+                st.markdown(result_card(f"{'z' if dist_is_z else 't'}-statistic", f"{stat:.4f}"), 
+                           unsafe_allow_html=True)
+            with cols[1]:
+                st.markdown(result_card("p-value", f"{p_val:.4g}"), unsafe_allow_html=True)
+            
+            if reject:
+                st.markdown(result_card("Decision", f"Reject H₀ at α = {alpha}", "result-card reject-card"), 
+                           unsafe_allow_html=True)
+            else:
+                st.markdown(result_card("Decision", f"Fail to reject H₀ at α = {alpha}", "result-card accept-card"), 
+                           unsafe_allow_html=True)
+            
+            with st.expander("📋 Details", expanded=False):
+                st.write(f"**x̄ = {xbar:.4f}** vs **μ₀ = {mu0:.4f}**")
+                st.write(f"**SE:** {se:.4f}")
+                st.write(f"**df:** {df}" if not dist_is_z else "**Distribution:** Normal (z)")
+                st.write(f"**Critical value:** {'±' if '≠' in alt else ''}{abs(crit):.4f}")
+            
+            results = {"Analysis": ["HT"], "n": [n], "x̄": [xbar], "μ₀": [mu0],
+                      "stat": [stat], "p-value": [p_val], "Reject": [reject]}
+
+    # ===== TWO-SAMPLE =====
+    elif inf_type == "Two-Sample" and n1 >= 2 and n2 >= 2:
+        se = np.sqrt(s1**2/n1 + s2**2/n2)
+        diff = xbar1 - xbar2
+        
+        # Welch df
+        df_num = (s1**2/n1 + s2**2/n2)**2
+        df_den = (s1**2/n1)**2/(n1-1) + (s2**2/n2)**2/(n2-1)
+        df = df_num / df_den
+        
+        if analysis_type == "Confidence Interval":
+            crit = norm.ppf(1 - (1 - conf_level)/2) if dist_is_z else t.ppf(1 - (1 - conf_level)/2, df)
+            margin = crit * se
+            lower, upper = diff - margin, diff + margin
+            
+            cols = st.columns(2)
+            with cols[0]:
+                st.markdown(result_card("Difference (x̄₁ − x̄₂)", f"{diff:.4f}"), unsafe_allow_html=True)
+            with cols[1]:
+                st.markdown(result_card(f"{conf_level*100:.0f}% Confidence Interval", 
+                                       f"[{lower:.4f}, {upper:.4f}]", "result-card ci-card"), unsafe_allow_html=True)
+            
+            with st.expander("📋 Details", expanded=False):
+                st.write(f"**x̄₁ = {xbar1:.4f}**, **x̄₂ = {xbar2:.4f}**")
+                st.write(f"**Standard Error (Welch):** {se:.4f}")
+                st.write(f"**df (Welch):** {df:.1f}")
+                st.write(f"**Margin of Error:** {margin:.4f}")
+            
+            results = {"Analysis": ["CI-2"], "x̄₁": [xbar1], "x̄₂": [xbar2],
+                      "Diff": [diff], "Lower": [lower], "Upper": [upper]}
+
+        else:  # Hypothesis Test
+            stat = diff / se
+            
+            if "≠" in alt:
+                p_val = 2 * (1 - (norm.cdf(abs(stat)) if dist_is_z else t.cdf(abs(stat), df)))
+                crit = norm.ppf(1 - alpha/2) if dist_is_z else t.ppf(1 - alpha/2, df)
+            elif ">" in alt:
+                p_val = 1 - (norm.cdf(stat) if dist_is_z else t.cdf(stat, df))
+                crit = norm.ppf(1 - alpha) if dist_is_z else t.ppf(1 - alpha, df)
+            else:
+                p_val = norm.cdf(stat) if dist_is_z else t.cdf(stat, df)
+                crit = -(norm.ppf(1 - alpha) if dist_is_z else t.ppf(1 - alpha, df))
+
+            reject = p_val <= alpha
+            
+            cols = st.columns(2)
+            with cols[0]:
+                st.markdown(result_card(f"{'z' if dist_is_z else 't'}-statistic", f"{stat:.4f}"), 
+                           unsafe_allow_html=True)
+            with cols[1]:
+                st.markdown(result_card("p-value", f"{p_val:.4g}"), unsafe_allow_html=True)
+            
+            if reject:
+                st.markdown(result_card("Decision", f"Reject H₀ at α = {alpha}", "result-card reject-card"), 
+                           unsafe_allow_html=True)
+            else:
+                st.markdown(result_card("Decision", f"Fail to reject H₀ at α = {alpha}", "result-card accept-card"), 
+                           unsafe_allow_html=True)
+            
+            with st.expander("📋 Details", expanded=False):
+                st.write(f"**x̄₁ = {xbar1:.4f}**, **x̄₂ = {xbar2:.4f}**")
+                st.write(f"**SE (Welch):** {se:.4f}")
+                st.write(f"**df (Welch):** {df:.1f}")
+            
+            results = {"Analysis": ["HT-2"], "x̄₁": [xbar1], "x̄₂": [xbar2],
+                      "stat": [stat], "p-value": [p_val], "Reject": [reject]}
+
+    # Download
+    if 'results' in locals():
+        df_out = pd.DataFrame(results)
+        buff = io.BytesIO()
+        with pd.ExcelWriter(buff, engine="xlsxwriter") as writer:
+            df_out.to_excel(writer, index=False)
+        st.download_button("📥 Download Results", data=buff.getvalue(),
+                          file_name="mean_inference.xlsx",
+                          mime="application/vnd.openxmlformats-officedocument.spreadsheetml.sheet")
+
+# ---------- Formulas (collapsed) ----------
+with st.expander("📚 Formulas & Theory", expanded=False):
+    st.markdown(r"""
+**One-Sample Mean**
+- SE: $s/\sqrt{n}$
+- CI: $\bar x \pm t_{\alpha/2, df} \cdot SE$
+- Test stat: $t = (\bar x - \mu_0)/SE$, $df = n-1$
+
+**Two Independent Means (Welch)**
+- SE: $\sqrt{s_1^2/n_1 + s_2^2/n_2}$
+- Welch df: $\dfrac{(s_1^2/n_1 + s_2^2/n_2)^2}{(s_1^2/n_1)^2/(n_1-1) + (s_2^2/n_2)^2/(n_2-1)}$
+- CI: $(\bar x_1 - \bar x_2) \pm t_{\alpha/2, df} \cdot SE$
+- Test stat: $t = (\bar x_1 - \bar x_2)/SE$
+
+**When to use z vs t:**
+- **z**: Large sample (n ≥ 30) or σ known
+- **t**: Small sample with σ unknown (assumes normal population)
 """)