So we know for a fact that Ho: \(\mu =3.94\). So you think, ok, the parameter is the population mean GPA for the state college, which we call \(\mu\), so then this statement is saying that \(\mu =3.94\), and since this mathematical statement contains the sign "=", then this must be the null hypothesis Ho. For example, you start reading a question and you find the following: "it has been claimed that the population mean GPA for some state college is 3.94". Indeed, sometimes, there are actually two claims about a population parameter.
Sometimes, things get a bit more complicated (but only a bit, I promise) when it comes down determining the null and alternative hypothesis from the setting of a question. \Īnother example: Things are not always that easy. Therefore, summarizing, in this case the null and alternative hypotheses would be: What is the null hypothesis then? Well, we know that the null and alternative hypotheses do not overlap, so we can say that the null hypothesis is the COMPLEMENT to what is expressed in the alternative hypothesis, so then in this case the null hypothesis is Ho: \(\mu \le 18\). So then in this case we have the alternative hypothesis is Ha: \(\mu >18\). Since the mathematical expression of the claim does not contain "=", then the claim must be the alternative hypothesis. And since the null hypothesis and alternative hypothesis cannot overlap, the only options for the sign of the alternative hypothesis are ">" or "18\)". The fourth point to keep in mind is the hypothesis of no effect, and it must contain the "=" sign, which means that the sign in the null hypothesis can be "\(\le\)", "=" or "\(\ge\)". This is VERY IMPORTANT, because once we have expressed the claim(s) provided mathematically, we need to take note of which mathematical sign is used (\(\le\), \(\ge\), =, ). Third, when reading the setting of an hypothesis testing problem, we need to identify any claim made about a population parameter, and express it in mathematical terms, such as \(\mu =2.3\), \(\mu \le 3\), \(\sigma >3.5\), etc. This implies that for the most part you can tell the null hypothesis if you know the alternative hypothesis, and vice versa, with some exceptions as we will see in the next paragraph. Second, you need to keep in mind that the null and alternative hypotheses DO NOT OVERLAP. Somewhere in the setting of the problem you will find where the hypotheses are stated. Typically, such information can be easily inferred from the context of the problem, but you need to know what to look for in order to get it right.įirst thing to keep in mind is the precise specification of the null and alternative hypotheses can be inferred from the wording on the actual problem.
One thing that can be tricky when attempting to solve a hypothesis testing problem is to establish precisely what theĪre.
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