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Granting loans to people who are good risks and denying loans to people who appears to be When evaluating a loan applicant, a financial officer is faced with the problem of

The level of significance of a hypothesis tests is the maximum Type I error probability allowed,Įxample 5. Is willing to tolerate committing the Type I error depending on the seriousness of committing the Therefore for a hypothesis we traditionally control .

For a fixed value of , in order to make  smaller we must increase the Reality we cannot make both smaller at the same time: if we try to make  smaller, then  gets The ideal decision rule should be such that both  and  are all as small as possible. Probability of not rejecting H 0 when is H 1 is true is called the Type II error Our main concern in the hypothesis test is committing one of the errors The probability of rejecting H 0 when H 0 is true is called the Type I error probability and denoted by . True State Decision H 0 H 1 Do not reject H 0 correct Type II error Reject H 0 Type I error correct We can summarize the decision of a hypothesis test in the following table. Thus rejection of the null hypothesis is a strong conclusion, while non-rejection of the null Hypothesis.” The null hypothesis is rejected if the evidence is beyond the reasonable doubt, and When the conclusion is not rejecting the null hypothesis, avoid using “accepting the null Rejecting the null hypothesis (hence accepting the alternative hypothesis) The conclusion drawn from a hypothesis test is either Whose side is determined by the alternative hypothesis. Hypothesis are called one sided tests because the values of the parameter claimed under theĪlternative hypothesis are on only one side of  0, and the rejection region is usually in one tail The last two sets of the null and alternative The rejection region is usually in both tails. The values of the parameter claimed under the alternative hypothesis are on both sides of  0, and The first set of the null and alternative hypothesis is called a two-sided test because The hypothesis  0 is called a simple hypothesis and the others are called composite The null and the alternative hypothesis take one of the following forms. During the election season, the incumbent is running agaist the challenger. There have been complaints that the company is short-weighting itsĮxample 4. A better business bureau is investigating a meat company that sells ground beef in 5. claims that their new product can increase A Corp.'s marketĮxample 3. When an athlete is tested for performance-enhancing drugs like steroids, we test two In theįollowing four examples, state the null and the alternative hypothesis.Įxample 1.

Requires substantial and convincing evidence and often called a researcher's hypothesis. The alternative hypothesis is an assertion that

Therefore, it is like a defendant in a court trial. The null hypothesis represents the status quo and will be given the benefit of the doubt. Very important to identify the null and the alternative hypothesis. Of a hypothesis and its competing hypothesis, one of them will be called the null hypothesis, denoted by H 0, and the other one will be called the alternative hypothesis, denoted by H 1. Given a hypothesis there exists a competing hypothesis, whether stated explicitly or not. A (statistical) hypothesis is a claim or statement (about the population parameter).