Hypothesis Testing
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This document outlines the steps for conducting a hypothesis test using the classical or critical value method for a one-sample case. It discusses the objectives, elements, and steps of hypothesis testing. The key elements are the null and alternative hypotheses, significance level, critical values of the test statistic, and the critical region used to determine whether to reject or fail to reject the null hypothesis. An example walks through applying the steps, which include formulating hypotheses, selecting a test statistic, establishing the critical region, computing the test statistic, and making a decision. The document emphasizes understanding hypothesis testing procedures and being able to apply the critical value method to real-life problems.
Hypothesis Testing
- 1. MR. FLORIAN E. MANZANILLA DEMO TEACHING
- 2. CONDUCTING HYPOTHESIS TEST USING CLASSICAL( Critical Value) METHOD (ONE –SAMPLE CASE) I. OBJECTIVES A. Content Standards The learner demonstrates understanding of key concepts of tests of hypotheses on the population mean and population proportion. B. Performance Standards The learner is able to perform appropriate tests of hypotheses involving the population mean and population proportion to make inferences in real-life problems in different disciplines C. Learning Competencies/Objectives At the end of the session, learners are expected to 1. Understand the underlying procedures in Hypothesis testing 2. Conduct a statistical test using the Critical value or classical method for one-sample case
- 3. ACTIVITY SHEET # 1. Read the following statements. Choose the letter of the best answer. 1. An Intelligent guess about the characteristics of a population is called: 2. The important numerical value in hypothesis testing is: a. parameter c. hypothesis 3. Under the normal curve, the middle part represents: b. acceptance region c. 0.05 5. Which of the following serves as a guide in deciding whether to reject or accept Ho : b. Decision rule
- 4. 6. Under the normal curve, when lines are drawn through this value, they separate the rejection region from the acceptance region a. -1.645 b. 0.01 10. Which of the following best represents a set of numerical data? c. variance a. confidence coefficient 8. In hypothesis testing, the probability of committing an error in rejecting a null hypothesis that is true is denoted by:
- 5. Central Limit Theorem (CLT) Accepting or Rejecting the Null Hypothesis Making decision to accept or reject the hypothesis depends on the test statistic value compared with the confidence coefficient (critical values) It states in part, that as sample size increases, the sampling distribution of the mean approaches the normal distribution provided that the sampling is random.
- 6. ELEMENTS OF HYPOTHESIS TESTING 1. Statistical hypothesis is an assumption about a population parameter. null hypothesis - it is hypothesis that there is no significant difference between specified populations. Denoted by : Ho
- 7. ELEMENTS OF HYPOTHESIS TESTING 2. Significance Level is the probability of making Type I error
- 8. ELEMENTS OF HYPOTHESIS TESTING 3. Type of Test
- 9. ELEMENTS OF HYPOTHESIS TESTING 4. Critical values of Z
- 10. ELEMENTS OF HYPOTHESIS TESTING
- 11. THE STEPS IN HYPOTHESIS TESTING USING THE CLASSICAL (CRITICAL VALUE) METHOD STEPS 1. Formulate the hypothesis 3. Select appropriate test statistic Ho and H1 , the two statements should be formulated in such a way that if one is true, the other is necessarily false) (If the level of significance is not identified it will always be set to be at . 05)
- 12. THE STEPS IN HYPOTHESIS TESTING USING THE CLASSICAL (CRITICAL VALUE) METHOD STEPS 4. Establish the critical region 5. Compute for the value of the statistical test. 6. Make a decision and, if possible draw a conclusion Depending on the type of alternative hypothesis, the critical region may be lying entirely on one tail or split into two equal parts on both tails of the distribution. Identify all the given and substitute to the appropriate statistic to find the value. (if the CV is within the region of rejection, we reject Ho and accept H1, if it lies outside the region of rejection, we accept Ho)
- 13. EXAMPLE # 1
- 14. Solutions STEPS ANSWERS 1. Formulate the hypothesis 3. Select appropriate test statistic
- 15. SOLUTIONS: STEPS 4. Establish the critical region 5. Compute for the value of the statistical test. 6. Make a decision and, if possible draw a conclusion Z >1.96 or Z < -1.96 The computed value of z is outside the region of rejection (-1.33 > -1.96). Therefore, we may accept the Ho. There is enough evidence to support the claim of the manufacturer that the average life of the bulbs it produces is 1000 hours.
- 16. Base from the examples that we have, What… 1.are the elements of hypothesis testing that we need to understand? 2. are the procedure/steps underlying the test of hypothesis. 3. generalization can you make regarding hypothesis testing? ABSTRACTION AND GENERALIZATION
- 17. EVALUATION :
- 18. “ There are two possible outcomes: if the result confirms the hypothesis, then you've made a measurement. If the result is contrary to the hypothesis, then you've made a discovery.” ~ Enrico Fermi CLOSURE