406 lines
17 KiB
TypeScript
406 lines
17 KiB
TypeScript
import React, { useRef, useState, useEffect } from "react";
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import {
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ArrowDown,
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Check,
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BookOpen,
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Target,
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Scale,
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Layers,
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} from "lucide-react";
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import SamplingVisualizerWidget from "../../../components/lessons/SamplingVisualizerWidget";
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import StudyDesignWidget from "../../../components/lessons/StudyDesignWidget";
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import ConfidenceIntervalWidget from "../../../components/lessons/ConfidenceIntervalWidget";
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import Quiz from "../../../components/lessons/Quiz";
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import {
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COLLECTING_DATA_QUIZ,
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INFERENCES_QUIZ_DATA,
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} from "../../../utils/constants";
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interface LessonProps {
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onFinish?: () => void;
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}
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const CollectingDataLesson: React.FC<LessonProps> = ({ onFinish }) => {
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const [activeSection, setActiveSection] = useState(0);
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const sectionsRef = useRef<(HTMLElement | null)[]>([]);
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const scrollToSection = (index: number) => {
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setActiveSection(index);
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sectionsRef.current[index]?.scrollIntoView({
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behavior: "smooth",
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block: "start",
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});
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};
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useEffect(() => {
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const observer = new IntersectionObserver(
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(entries) => {
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entries.forEach((entry) => {
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if (entry.isIntersecting) {
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const index = sectionsRef.current.indexOf(
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entry.target as HTMLElement,
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);
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if (index !== -1) setActiveSection(index);
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}
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});
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},
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{ rootMargin: "-20% 0px -60% 0px" },
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);
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sectionsRef.current.forEach((section) => {
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if (section) observer.observe(section);
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});
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return () => observer.disconnect();
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}, []);
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const SectionMarker = ({
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index,
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title,
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icon: Icon,
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}: {
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index: number;
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title: string;
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icon: any;
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}) => {
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const isActive = activeSection === index;
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const isPast = activeSection > index;
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return (
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<button
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onClick={() => scrollToSection(index)}
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className={`flex items-center gap-3 p-3 w-full rounded-lg transition-all ${isActive ? "bg-white shadow-md border border-amber-100" : "hover:bg-slate-100"}`}
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>
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<div
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className={`w-8 h-8 rounded-full flex items-center justify-center shrink-0 ${isActive ? "bg-amber-600 text-white" : isPast ? "bg-amber-400 text-white" : "bg-slate-200 text-slate-500"}`}
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>
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{isPast ? (
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<Check className="w-4 h-4" />
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) : (
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<Icon className="w-4 h-4" />
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)}
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</div>
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<div className="text-left">
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<p
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className={`text-sm font-bold ${isActive ? "text-amber-900" : "text-slate-600"}`}
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>
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{title}
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</p>
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</div>
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</button>
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);
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};
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const allQuizzes = [...COLLECTING_DATA_QUIZ, ...INFERENCES_QUIZ_DATA];
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return (
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<div className="flex flex-col lg:flex-row min-h-screen">
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<aside className="w-full lg:w-64 lg:fixed lg:top-20 lg:bottom-0 lg:overflow-y-auto p-4 border-r border-slate-200 bg-slate-50 lg:bg-transparent z-0 hidden lg:block">
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<nav className="space-y-2">
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<SectionMarker index={0} title="Sampling & Bias" icon={Scale} />
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<SectionMarker index={1} title="Study Design" icon={Layers} />
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<SectionMarker index={2} title="Confidence Intervals" icon={Target} />
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<SectionMarker index={3} title="Practice" icon={BookOpen} />
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</nav>
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</aside>
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<div className="flex-1 lg:ml-64 p-6 md:p-12 max-w-4xl mx-auto">
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{/* Section 1: Sampling & Bias */}
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<section
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ref={(el) => {
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sectionsRef.current[0] = el;
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}}
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className="min-h-screen flex flex-col justify-center mb-24 pt-20 lg:pt-0"
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>
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<h2 className="text-4xl font-extrabold text-slate-900 mb-6">
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Sampling & Bias
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</h2>
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<div className="prose prose-slate text-lg text-slate-600 mb-8">
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<p>
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To generalize results to a population, your sample must be{" "}
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<strong>representative</strong>. The best way to achieve this is
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through <strong>random sampling</strong>. Convenience samples
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(e.g., asking friends) introduce <strong>bias</strong> — they
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systematically over- or under-represent parts of the population.
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</p>
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<div className="mt-5 overflow-x-auto">
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<table className="w-full text-sm border-collapse">
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<thead>
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<tr className="bg-amber-100 text-amber-900">
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<th className="border border-amber-300 px-3 py-2 text-left font-bold">
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Method
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</th>
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<th className="border border-amber-300 px-3 py-2 text-left font-bold">
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Description
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</th>
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<th className="border border-amber-300 px-3 py-2 text-left font-bold">
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Bias Risk
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</th>
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</tr>
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</thead>
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<tbody className="text-slate-700">
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<tr className="bg-white">
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<td className="border border-slate-200 px-3 py-2 font-semibold">
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Simple Random
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</td>
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<td className="border border-slate-200 px-3 py-2">
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Every individual has an equal chance of selection
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</td>
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<td className="border border-slate-200 px-3 py-2 text-emerald-700 font-semibold">
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Very Low
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</td>
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</tr>
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<tr className="bg-slate-50">
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<td className="border border-slate-200 px-3 py-2 font-semibold">
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Stratified
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</td>
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<td className="border border-slate-200 px-3 py-2">
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Population divided into subgroups; random sample from each
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</td>
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<td className="border border-slate-200 px-3 py-2 text-emerald-700 font-semibold">
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Very Low
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</td>
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</tr>
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<tr className="bg-white">
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<td className="border border-slate-200 px-3 py-2 font-semibold">
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Cluster
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</td>
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<td className="border border-slate-200 px-3 py-2">
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Randomly select entire subgroups (e.g., classrooms)
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</td>
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<td className="border border-slate-200 px-3 py-2 text-amber-700 font-semibold">
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Low–Medium
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</td>
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</tr>
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<tr className="bg-slate-50">
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<td className="border border-slate-200 px-3 py-2 font-semibold">
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Systematic
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</td>
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<td className="border border-slate-200 px-3 py-2">
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Select every kth individual from a list
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</td>
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<td className="border border-slate-200 px-3 py-2 text-amber-700 font-semibold">
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Low–Medium
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</td>
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</tr>
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<tr className="bg-white">
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<td className="border border-slate-200 px-3 py-2 font-semibold">
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Convenience
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</td>
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<td className="border border-slate-200 px-3 py-2">
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Whoever is easiest to reach (friends, passersby)
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</td>
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<td className="border border-slate-200 px-3 py-2 text-rose-700 font-semibold">
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High
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</td>
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</tr>
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</tbody>
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</table>
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</div>
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<div className="mt-4 grid md:grid-cols-2 gap-4">
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<div className="bg-emerald-50 border border-emerald-200 rounded-xl p-4">
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<p className="font-bold text-emerald-900 mb-1">
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Representative Sample
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</p>
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<p className="text-sm text-slate-700">
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Mirrors the population in all key characteristics. Allows you
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to generalize findings to the whole group. Achieved through
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random selection.
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</p>
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</div>
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<div className="bg-rose-50 border border-rose-200 rounded-xl p-4">
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<p className="font-bold text-rose-900 mb-1">Biased Sample</p>
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<p className="text-sm text-slate-700">
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Systematically excludes or over-includes certain groups.
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Results cannot be generalized. Watch for voluntary response
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and convenience sampling.
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</p>
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</div>
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</div>
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<div className="mt-4 p-3 bg-amber-50 border-l-4 border-amber-500 rounded-r-lg text-sm">
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<strong className="text-amber-900">Margin of Error:</strong> Even
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a well-designed random sample has some uncertainty. The margin of
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error (e.g., ±3%) tells you the range where the true population
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value likely falls. Larger samples produce smaller margins of
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error.
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</div>
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</div>
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<SamplingVisualizerWidget />
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<button
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onClick={() => scrollToSection(1)}
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className="mt-12 group flex items-center text-amber-600 font-bold hover:text-amber-800 transition-colors"
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>
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Next: Study Design{" "}
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<ArrowDown className="ml-2 w-5 h-5 group-hover:translate-y-1 transition-transform" />
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</button>
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</section>
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{/* Section 2: Study Design */}
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<section
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ref={(el) => {
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sectionsRef.current[1] = el;
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}}
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className="min-h-screen flex flex-col justify-center mb-24"
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>
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<h2 className="text-4xl font-extrabold text-slate-900 mb-6">
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Study Design: Generalization vs Causation
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</h2>
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<div className="prose prose-slate text-lg text-slate-600 mb-8">
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<p>
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Two concepts are critical here. <strong>Random sampling</strong>{" "}
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determines whether you can extend your conclusions to the broader
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population. <strong>Random assignment</strong> (used in
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experiments) determines whether you can claim cause-and-effect.
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</p>
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<div className="mt-5 overflow-x-auto">
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<table className="w-full text-sm border-collapse">
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<thead>
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<tr className="bg-amber-100 text-amber-900">
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<th className="border border-amber-300 px-3 py-2"></th>
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<th className="border border-amber-300 px-3 py-2 text-center font-bold">
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Random Assignment? YES
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</th>
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<th className="border border-amber-300 px-3 py-2 text-center font-bold">
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Random Assignment? NO
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</th>
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</tr>
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</thead>
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<tbody className="text-slate-700">
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<tr className="bg-white">
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<td className="border border-slate-200 px-3 py-2 font-bold bg-amber-50 text-amber-900">
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Random Sampling? YES
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</td>
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<td className="border border-slate-200 px-3 py-2 text-center bg-emerald-50 text-emerald-800 font-semibold">
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Generalize + Cause & Effect
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</td>
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<td className="border border-slate-200 px-3 py-2 text-center bg-blue-50 text-blue-800 font-semibold">
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Generalize only
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</td>
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</tr>
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<tr className="bg-slate-50">
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<td className="border border-slate-200 px-3 py-2 font-bold bg-amber-50 text-amber-900">
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Random Sampling? NO
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</td>
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<td className="border border-slate-200 px-3 py-2 text-center bg-purple-50 text-purple-800 font-semibold">
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Cause & Effect only (for this group)
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</td>
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<td className="border border-slate-200 px-3 py-2 text-center bg-rose-50 text-rose-800 font-semibold">
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Neither — observe only
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</td>
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</tr>
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</tbody>
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</table>
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</div>
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<div className="mt-4 p-3 bg-amber-50 border-l-4 border-amber-500 rounded-r-lg text-sm">
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<strong className="text-amber-900">SAT Key Rule:</strong>{" "}
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Observational studies (no random assignment) can show{" "}
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<em>association</em> but never <em>causation</em>. Only randomized
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controlled experiments can establish cause-and-effect.
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</div>
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</div>
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<StudyDesignWidget />
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<button
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onClick={() => scrollToSection(2)}
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className="mt-12 group flex items-center text-amber-600 font-bold hover:text-amber-800 transition-colors"
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>
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Next: Confidence Intervals{" "}
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<ArrowDown className="ml-2 w-5 h-5 group-hover:translate-y-1 transition-transform" />
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</button>
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</section>
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{/* Section 3: Confidence Intervals & Comparing Groups */}
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<section
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ref={(el) => {
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sectionsRef.current[2] = el;
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}}
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className="min-h-screen flex flex-col justify-center mb-24"
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>
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<h2 className="text-4xl font-extrabold text-slate-900 mb-6">
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Confidence Intervals & Comparing Groups
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</h2>
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<div className="prose prose-slate text-lg text-slate-600 mb-8">
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<p>
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A <strong>Confidence Interval</strong> (Estimate ± Margin of
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Error) gives a range where the true population value likely lies.
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When comparing two groups, check for <strong>overlap</strong> — if
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the intervals do not overlap, you can conclude a significant
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difference.
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</p>
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<div className="mt-4 bg-amber-50 border border-amber-200 rounded-xl p-5 space-y-3">
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<p className="font-bold text-amber-900">
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Key Rules for Confidence Intervals
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</p>
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<div className="grid md:grid-cols-2 gap-3 text-sm">
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<div className="bg-white rounded-lg p-3 border border-amber-100">
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<p className="font-bold text-amber-800 mb-1">
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Intervals Overlap
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</p>
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<p className="text-slate-700">
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Cannot claim a significant difference between the two
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groups.
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</p>
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</div>
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<div className="bg-white rounded-lg p-3 border border-amber-100">
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<p className="font-bold text-amber-800 mb-1">
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Intervals Don't Overlap
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</p>
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<p className="text-slate-700">
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There is a significant difference — the groups are
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statistically distinct.
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</p>
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</div>
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</div>
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<div className="bg-amber-100 rounded-lg p-3 text-sm">
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<p className="font-bold text-amber-900 mb-1">
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Larger Samples → Smaller Margin of Error
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</p>
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<p className="text-slate-700">
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Increasing the sample size narrows the confidence interval,
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giving you a more precise estimate.
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</p>
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</div>
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</div>
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</div>
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<ConfidenceIntervalWidget />
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<button
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onClick={() => scrollToSection(3)}
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className="mt-12 group flex items-center text-amber-600 font-bold hover:text-amber-800 transition-colors"
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>
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Next: Practice Quiz{" "}
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<ArrowDown className="ml-2 w-5 h-5 group-hover:translate-y-1 transition-transform" />
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</button>
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</section>
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{/* Section 4: Quiz */}
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<section
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ref={(el) => {
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sectionsRef.current[3] = el;
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}}
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className="min-h-screen flex flex-col justify-center"
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>
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<h2 className="text-4xl font-extrabold text-slate-900 mb-8">
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Practice Time
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</h2>
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{allQuizzes.map((quiz, idx) => (
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<div key={`quiz-${idx}`} className="mb-12">
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<Quiz data={quiz} />
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</div>
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))}
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<div className="p-8 bg-amber-900 rounded-2xl text-white text-center mt-12">
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<h3 className="text-2xl font-bold mb-4">Topic Mastered!</h3>
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<button
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onClick={onFinish}
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className="px-6 py-3 bg-white text-amber-900 font-bold rounded-full hover:bg-amber-50 transition-colors"
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>
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Finish Lesson ✓
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</button>
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</div>
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</section>
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</div>
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</div>
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);
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};
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export default CollectingDataLesson;
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