9.7
Toma de decisiones: método tradicional
El proceso de prueba de hipótesis basado en el método tradicional incluye calcular el valor crítico, probar el valor de la estadística de prueba utili…
El método tradicional o clásico implica el uso del valor crítico para concluir la prueba de hipótesis.
Como primer paso, una hipótesis se enuncia y expresa simbólicamente de la siguiente manera.
Para la proporción, media o desviación estándar de una población, las hipótesis nula y alternativa se expresan de la siguiente manera.
Además, se obtiene un valor crítico para el parámetro elegido en las hipótesis a un nivel de significación predeterminado específico α. Para la proporción, la media o la desviación estándar, estos valores críticos en α son los valores z, t o chi-cuadrado, respectivamente, que se calculan utilizando las distribuciones z, t o chi-cuadrado.
A continuación, se traza el valor crítico para demarcar la región crítica en la distribución de probabilidad.
Además, el estadístico de prueba se calcula utilizando los datos de la muestra y se traza en la curva de distribución de probabilidad.
La hipótesis nula se rechaza cuando el valor del estadístico de prueba se encuentra dentro de la región crítica. Sin embargo, no lo rechazamos cuando el estadístico de prueba cae fuera de la región crítica.
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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.