![graph a rejection region in minitab express graph a rejection region in minitab express](https://i.ytimg.com/vi/5A0QjTXCxLE/maxresdefault.jpg)
If the sample mean is slightly less than 75 then we would logically attribute the difference to sampling error and also not reject H 0 either. If the sample mean is 75 or greater then we certainly would not reject H 0 (since there is no issue with an emergency respirator delivering air even longer than claimed). Think of the respirator example, for which the null hypothesis is H 0 : μ = 75, the claim that the average time air is delivered for all respirators is 75 minutes. The first step in hypothesis testing is to identify the null and alternative hypotheses.įigure 8.1 The Density Curve for X - if H 0 Is True So in the introductory example about the respirators, we stated the manufacturer’s claim as “the average is 75 minutes” instead of the perhaps more natural “the average is at least 75 minutes,” essentially reducing the presentation of the null hypothesis to its worst case. This is the same as always stating the null hypothesis in the least favorable light. The claim expressed with an equality is the null hypothesis.
![graph a rejection region in minitab express graph a rejection region in minitab express](https://support.minitab.com/en-us/minitab-express/1/one_z_fat_content.xml_Graph_cmd2o3.png)
Thus in order to make the null and alternative hypotheses easy for the student to distinguish, in every example and problem in this text we will always present one of the two competing claims about the value of a parameter with an equality. It is always true that if the null hypothesis is retained for its least favorable value, then it is retained for every other value. If the claim were made this way, then the null hypothesis would be H 0 : μ ≤ 127.50, and the value $127.50 given in the example would be the one that is least favorable to the publisher’s claim, the null hypothesis. In Note 8.8 "Example 1", the textbook example, it might seem more natural that the publisher’s claim be that the average price is at most $127.50, not exactly $127.50. Since to contain either more fat than desired or to contain less fat than desired are both an indication of a faulty production process, the alternative hypothesis in this situation is that the mean is different from 8.0, so H a : μ ≠ 8.0.
![graph a rejection region in minitab express graph a rejection region in minitab express](https://media.cheggcdn.com/media/444/44490a50-705b-42e7-9d9b-8a970f1f8617/image.png)
Thus the null hypothesis is H 0 : μ = 8.0. The default option is to assume that the product contains the amount of fat it was formulated to contain unless there is compelling evidence to the contrary.
![graph a rejection region in minitab express graph a rejection region in minitab express](https://media.springernature.com/original/springer-static/image/chp%3A10.1007%2F978-3-030-55156-8_9/MediaObjects/217454_3_En_9_Fig1_HTML.png)
State the relevant null and alternative hypotheses. The quality control department samples the product periodically to insure that the production process is working as designed. The recipe for a bakery item is designed to result in a product that contains 8 grams of fat per serving. The alternative hypothesis in the example is the contradictory statement H a : μ ,” or with the symbol “≠” The following two examples illustrate the latter two cases. In the example of the respirators, we would believe the claim of the manufacturer unless there is reason not to do so, so the null hypotheses is H 0 : μ = 75. The null hypothesis typically represents the status quo, or what has historically been true. Fail to reject H 0 (and therefore fail to accept H a).Reject H 0 (and therefore accept H a), or.The end result of a hypotheses testing procedure is a choice of one of the following two possible conclusions: is a statistical procedure in which a choice is made between a null hypothesis and an alternative hypothesis based on information in a sample. Hypothesis testing A statistical procedure in which a choice is made between a null hypothesis and a specific alternative hypothesis based on information in a sample. Their sampling is done to perform a test of hypotheses, the subject of this chapter. The agency is not necessarily interested in the actual value of μ, just whether it is as claimed. But the sampling done by the government agency has a somewhat different objective, not so much to estimate the population mean μ as to test an assertion-or a hypothesis A statement about a population parameter.-about it, namely, whether it is as large as 75 or not. In the sampling that we have studied so far the goal has been to estimate a population parameter. To do so it would select a random sample of respirators, compute the mean time that they deliver pure air, and compare that mean to the asserted time 75 minutes. A government regulatory agency is charged with testing such claims, in this case to verify that the average time is not less than 75 minutes. A manufacturer of emergency equipment asserts that a respirator that it makes delivers pure air for 75 minutes on average.