Si la hipótesis nula establece que la media es igual a 0, ¿cuál es la hipótesis alterna?

Understand the Problem

La pregunta es sobre pruebas de hipótesis en estadística. Especificamente, pregunta cuál es la hipótesis alternativa correcta cuando la hipótesis nula establece que la media es igual a 0. La hipótesis alternativa es la declaración que se está tratando de encontrar evidencia para respaldar.

Answer

$\mu \neq 0$

Steps to Solve

Understanding the Null Hypothesis The null hypothesis ($H_0$) states that the population mean, denoted by $\mu$, is equal to 0. Mathematically, this is written as: $H_0: \mu = 0$
Understanding the Alternative Hypothesis The alternative hypothesis ($H_1$ or $H_a$) is what we are trying to find evidence for. It contradicts the null hypothesis. In this case, since the null hypothesis states that the mean is equal to 0, the alternative hypothesis can take one of three forms.

The mean is less than 0: $\mu < 0$
The mean is greater than 0: $\mu > 0$
The mean is not equal to 0: $\mu \neq 0$

Determining the correct alternative hypothesis The question does not specify a direction (less than or greater than). Therefore, a two-tailed alternative hypothesis is appropriate. This means we are testing whether the mean is simply different from 0 (either greater or less than).
Selecting the correct option Given the options, the correct alternative hypothesis is that the mean is not equal to 0. $\mu \neq 0$

$\mu \neq 0$

More Information

In hypothesis testing, stating the null and alternative hypotheses correctly is crucial for performing accurate statistical tests. The alternative hypothesis guides the type of test and interpretation of results.

Tips

A common mistake is choosing a one-tailed test (either $\mu < 0$ or $\mu > 0$) when a two-tailed test ($\mu \neq 0$) is more appropriate. This usually happens when the problem does not suggest any specific direction of the effect.

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