Tests of hypothesis Statistical hypothesis definition: A statistical hypothesis is an assertion or conjecture on or more population.

Tests of hypothesis The null and alternative hypothesis: The structure of hypothesis testing will be formulated with the term null hypothesis, which refers to any hypothesis, we wish to test. It’s denoted by H 0.

Tests of hypothesis The rejection of H 0 leads to acceptance alternative hypothesis which denoted by H a.

Tests of hypothesis Type I error It is rejection of null hypothesis when it is true.

Tests of hypothesis Type II error Non rejection of the null hypothesis when it is false. Size of test: It is the probability of making a type I error.

Tests of hypothesis Which is better type I error or type II error? To answer the above question we can imagine this situation: H 0 : The person is unguilty”الشخص برئ” H a : The person is guilty”الشخص مدان” Type I error is the person is guilty although he is unguilty “Reject H 0 ” Type II error reject H 0 when it is false. So Type II error is better than Type I error.

Tests of hypothesis The power of test: It is the probability of rejection H 0 given that a specific alternative is true. P-value: A P-value is the lowest level of significance at which the observed value of the test statistic is significant.

Tests of hypothesis Example 1: Suppose that an allergist wishes to test the hypothesis that at least 30% of public is allergic to some cheese products. Explain how the allergic could commit. 1.Type I error. 2.Type II error.

Tests of hypothesis Solution: H 0 : >= 30% of people suffering from cheese product allergy. H a : < 30% of people suffering from cheese product allergy. Type I error: Reject H 0 although it is true mean that less than 30% of cheese product cause allergic. Type II error: At least 30% of people have allergic from cheese product although they are less than 30%.

Tests of hypothesis Example 2: A fabric manufacturer believes that the proportion of orders for raw material arriving late is p=0.6. If a random sample of 10 orders. Show that 3 or fewer arrived late The hypothesis that p = 0.6 should be rejected in favor of the alternative p < 0.6. use binomial distribution. 1.Find the probability of committing a type I error if the true hypothesis is true. 2.Find the probability of committing a type II error for alternative p=0.3, p = 0.4, p= 0.5.

Tests of hypothesis Solution:

Tests of hypothesis Solution:

Tests of hypothesis 2 Then

Tests of hypothesis 2

2