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

2. 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.

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

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

5. 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.

6. 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.

7. 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.

8. 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.

9. 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%.

10. 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.

11. Tests of hypothesis Solution:

12. Tests of hypothesis Solution:

13. Tests of hypothesis 2 Then

14. Tests of hypothesis 2

15. 2