We merely state that there is enough evidence to behave one way or the other. If we do not reject the null hypothesis, we do not prove that the null hypothesis is true.If we reject the null hypothesis, we do not prove that the alternative hypothesis is true.This is a very important distinction! We make our decision based on evidence not on 100% guaranteed proof. And, we "behave as if" the defendant is innocent we do not "prove" that the defendant is innocent. We either "reject the null hypothesis" or we "fail to reject the null hypothesis."ĭid you notice the use of the phrase "behave as if" in the previous discussion? We "behave as if" the defendant is guilty we do not "prove" that the defendant is guilty. In statistics, we always make one of two decisions. We behave as if the defendant is innocent. If there is insufficient evidence, then the jury does not reject the null hypothesis.If the jury finds sufficient evidence - beyond a reasonable doubt - to make the assumption of innocence refutable, the jury rejects the null hypothesis and deems the defendant guilty.The jury then makes a decision based on the available evidence: In statistics, the data are the evidence. The prosecution team then collects evidence - such as finger prints, blood spots, hair samples, carpet fibers, shoe prints, ransom notes, and handwriting samples - with the hopes of finding "sufficient evidence" to make the assumption of innocence refutable. That is, the null hypothesis is always our initial assumption. In statistics, we always assume the null hypothesis is true. H 0: Defendant is not guilty (innocent).In the practice of statistics, we make our initial assumption when we state our two competing hypotheses - the null hypothesis ( H 0) and the alternative hypothesis ( H A). Our criminal justice system assumes "the defendant is innocent until proven guilty." That is, our initial assumption is that the defendant is innocent. One place where you can consistently see the general idea of hypothesis testing in action is in criminal trials held in the United States. That is, in the practice of statistics, if the evidence (data) we collected is unlikely in light of the initial assumption, then we reject our initial assumption. In statistics, we generally don't make claims that require us to believe that a very unusual event happened. or the researcher's initial assumption is incorrect.either the researcher's initial assumption is correct and he experienced a very unusual event.There is not enough evidence to do otherwise. If it is likely, then the researcher does not reject his initial assumption that the average adult body temperature is 98.6 degrees.It is either likely or unlikely that the researcher would collect the evidence he did given his initial assumption that the average adult body temperature is 98.6 degrees: Then, the researcher uses the data he collected to make a decision about his initial assumption. The average body temperature of the 130 sampled adults is 98.25 degrees. In doing so, he selects a random sample of 130 adults. Then, the researcher went out and tried to find evidence that refutes his initial assumption. That is, the researcher wants an answer to the question: "Is the average adult body temperature 98.6 degrees? Or is it lower?" To answer his research question, the researcher starts by assuming that the average adult body temperature was 98.6 degrees F. A researcher hypothesized that the average adult body temperature is lower than the often-advertised 98.6 degrees F. Consider the population of many, many adults.
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