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統計学について教えてください。
Peechyanの回答
- Peechyan
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まず、この問題のタイプなんですけど、統計学では2項分布(Binominal Distribution)とか、2項確率といわれるジャンルの問題です。平たく言うと、’Yes / No’とか’裏/表’などの二通りの答えの可能性がある場合にこの分布が適用されます。 ■ 手計算 ○ まず、母集団(10人)の中の好き、好きでないの確率を求めます。 ハニーが好きという事象をHとおく。よって、P(H)=6[人]/10[人]=3/5 となる。 ハニーが好きでないという事象をHバーとおく(Hの上に横棒が書いてある)。 P(Hバー)=1-3/5=2/5 ○ 次に、母集団から’ランダムに’選ばれた4人の中での二項確率を求めます。 母集団(10[人])において、P(H)=3/5、P(Hバー)=2/5であるから、 この10名のうちからランダムに4人のサンプルを選ぶと、インタビューを受ける4名が、 2名は好きと答えた人、残り2名は嫌いと答えた人になる可能性は2項分布Bin(4, 3/5)に従う。 よって、P(4人のうち好きと答える人が2人) = 4C2 * (3/5)^2 * (2/5)^4-2 = 6*9/25*4/25=216/625 = 0.3456 ＊ ここで、4C2は、組み合わせを表しており、2項係数とも呼ばれます。 ■ 同じ事をエクセルでやる： エクセルでは、二項分布の計算は、BINOMDIST関数を使います。 P(4人のうち好きと答える人が2人)=BINOMDIST(2,4,0.6,FALSE) 同じ答えが出ました。 なお、関数の書式は、BINOMDIST(成功数、試行回数、成功率、関数形式)となっており、 (1) 成功数：好きと答える人が2人なので、２ (2) 試行回数：サンプル数が4人なので、４ (3) 成功率：ハニーが好きな人の確率 P(H)=3/5=0.6 となります。 (4) 関数形式：Trueとすると、累積確率になるので、この場合はFalseにします。
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