Si la hipótesis nula establece que la media es igual a 0, ¿cuál es la hipótesis alterna?
Understand the Problem
La pregunta se refiere a las pruebas de hipótesis en estadística. Específicamente, pregunta cuál sería la hipótesis alternativa apropiada si la hipótesis nula establece que la media es igual a 0. La hipótesis alternativa es la afirmación que se intenta probar como verdadera en contraposición a la hipótesis nula.
Answer
$\mu \neq 0$
Answer for screen readers
$\mu \neq 0$
Steps to Solve
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Understanding the Null Hypothesis The null hypothesis states that the population mean (μ) is equal to 0. In mathematical terms, this is written as: $H_0: \mu = 0$
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Understanding the Alternative Hypothesis The alternative hypothesis is what we are trying to find evidence for. In this case, we are considering a two-tailed test, meaning we want to determine if the population mean is different from 0. It could be either greater or lesser than zero.
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Choosing the Correct Alternative Hypothesis Since we are testing if the mean is different from 0, the alternative hypothesis should reflect this. The symbol "≠" means "not equal to." Thus, the correct alternative hypothesis is that the population mean is not equal to 0. In mathematical terms: $H_1: \mu \neq 0$ This alternative hypothesis covers both cases: $\mu < 0$ and $\mu > 0$.
$\mu \neq 0$
More Information
The alternative hypothesis is set up to contradict the null hypothesis. The null hypothesis often states that there is "no effect" or "no difference". The alternative hypothesis challenges that perspective, suggesting that there actually is an effect or difference to measure.
Tips
A common mistake is to confuse the null and alternative hypotheses. The null hypothesis is a statement that we assume to be true unless we have strong evidence against it. The alternative hypothesis is what we are trying to find evidence for. Another mistake would be to select $u < 0$ or $u > 0$ if the question asks generally if it is different than 0.
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