9.7
意思決定: 従来の方法
従来の方法に基づく仮説検定のプロセスには、臨界値の計算、サンプル データを使用した検定統計量の値の検定、およびこれらの値の解釈が含まれます。
まず、母集団パラメータに関する具体的な主張がリサーチクエスチョンに基づいて決定され、簡単な形式で記述されます。さらに、この主張に対して反対の意見も述べられてい…
従来の方法または古典的な方法では、臨界値を使用して仮説検定を結論付けます。
最初のステップとして、次のように仮説を述べ、象徴的に表現します。
母集団の比率、平均、または標準偏差について、帰無仮説と対立仮説は次のように表されます。
さらに、仮説内の選択されたパラメータについて、特定の所定の有意水準αで臨界値が取得されます。比率、平均、または標準偏差の場合、αでのこれらの重要な値は、それぞれ z、t、または chi 2 乗値であり、z、t、または chi 2 乗分布を使用して計算されます。
次に、確率分布の臨界領域を区切るために、臨界値がプロットされます。
さらに、検定統計量はサンプルデータを使用して計算され、確率分布曲線にプロットされます。
帰無仮説は、検定統計値がクリティカル領域内にある場合に棄却されます。ただし、検定統計量がクリティカル領域外にある場合は、それを棄却できません。
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Q1: What are the main steps in the traditional method of hypothesis testing?
The traditional method involves stating null and alternative hypotheses symbolically, obtaining a critical value at a predetermined significance level, calculating a test statistic from sample data, and plotting both on a probability distribution. The null hypothesis is rejected if the test statistic falls within the critical region; otherwise, you fail to reject it.
Q2: How do you express null and alternative hypotheses in the traditional method?
Null and alternative hypotheses are expressed symbolically based on the population parameter being tested. By convention, the null hypothesis contains an equality symbol, while the alternative hypothesis contains >, <, or ≠ symbols. The null hypothesis represents a neutral statement, while the alternative hypothesis may have a specific direction or represent the original research claim.
Q3: What test statistic should you use when testing a claim about a population mean with unknown population standard deviation?
When the population standard deviation is unknown, use the t statistic to test a claim about a population mean. The t statistic is calculated from sample data and compared against the critical value obtained from the t distribution at your chosen significance level.
Q4: What significance level should you choose for hypothesis testing?
Common significance levels follow a general convention of 95% confidence (α = 0.05) or 99% confidence (α = 0.01). The significance level determines the critical value and defines the critical region boundaries on the probability distribution where you reject the null hypothesis.
Q5: How do you decide whether to reject the null hypothesis using the traditional method?
Compare your calculated test statistic to the critical region on the probability distribution. If the test statistic falls within the critical region, reject the null hypothesis. If it falls outside the critical region, fail to reject the null hypothesis. This decision does not require calculating the p-value.
Q6: What is the difference between the z statistic, t statistic, and chi-square statistic in hypothesis testing?
The z statistic tests claims about proportions or means when population standard deviation is known. The t statistic tests claims about means when population standard deviation is unknown. The chi-square statistic tests claims about population variance or standard deviation. Each uses its respective distribution to determine critical values.
Q7: Why is the critical value important in the traditional method of hypothesis testing?
The critical value demarcates the critical region on the probability distribution at your chosen significance level. It serves as the boundary for decision-making: if your test statistic exceeds this boundary, you reject the null hypothesis. Critical values are obtained from z, t, or chi-square tables depending on your test statistic type.