For this reason, a weighted coin is not fair. We conducted a simulation in which each sample consists of 40 flips of a fair coin. Here is a simulated sampling distribution for the proportion of heads in 2, samples. Results ranged from 0. In general, if the null hypothesis is true, the significance level gives the probability of making a type I error. This is a problem! Moore in Basic Practice of Statistics 4th ed.
Freeman, :. This is an example of a probable type I error. So the conclusion that this one type of cancer is related to cell phone use is probably just a result of random chance and not an indication of an association. Click here to see a fun cartoon that illustrates this same idea. Telepathy is the ability to read minds. Researchers used Zener cards in the early s for experimental research into telepathy. This is repeated 40 times, and the proportion of correct responses is recorded.
So in 40 tries, 8 correct guesses, a proportion of 0. But of course there will be variability even when someone is just guessing. Thirteen or more correct in 40 tries, a proportion of 0. When people perform this well on the telepathy test, we conclude their performance is not due to chance and take it as an indication of the ability to read minds.
Before we get into the details, we want to step back and think more generally about hypothesis testing. We close our introduction to hypothesis testing with a helpful analogy. When a defendant stands trial for a crime, he or she is innocent until proven guilty.
It is the job of the prosecution to present evidence showing that the defendant is guilty beyond a reasonable doubt. It is the job of the defense to challenge this evidence to establish a reasonable doubt. The jury weighs the evidence and makes a decision. In a courtroom, the person is assumed innocent until proven guilty. In a hypothesis test, we assume the null hypothesis is true until the data proves otherwise. The two possible verdicts are similar to the two conclusions that are possible in a hypothesis test.
Reject the null hypothesis: When we reject a null hypothesis, we accept the alternative hypothesis. This is like a guilty verdict. The choice of symbol depends on the wording of the hypothesis test.
This practice is acceptable because we only make the decision to reject or not reject the null hypothesis. State the null and alternative hypotheses. We want to test whether the mean GPA of students in American colleges is different from 2. The null and alternative hypotheses are:. We want to test whether the mean height of eighth graders is 66 inches. We want to test if college students take less than five years to graduate from college, on the average. We want to test if it takes fewer than 45 minutes to teach a lesson plan.
In an issue of U. News and World Report , an article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third pass.
The same article stated that 6. Test if the percentage of U. In a hypothesis test , sample data is evaluated in order to arrive at a decision about some type of claim. Now that we have reviewed the critical value and P -value approach procedures for each of three possible hypotheses, let's look at three new examples — one of a right-tailed test, one of a left-tailed test, and one of a two-tailed test.
The good news is that, whenever possible, we will take advantage of the test statistics and P -values reported in statistical software, such as Minitab, to conduct our hypothesis tests in this course.
Breadcrumb Home reviews statistical concepts hypothesis testing p value approach. Specifically, the four steps involved in using the P -value approach to conducting any hypothesis test are: Specify the null and alternative hypotheses. Using the sample data and assuming the null hypothesis is true, calculate the value of the test statistic. Using the known distribution of the test statistic, calculate the P -value : "If the null hypothesis is true, what is the probability that we'd observe a more extreme test statistic in the direction of the alternative hypothesis than we did?
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