Statistical Analysis for IE 2 PDF

Republic of the Philippines POLYTECHNIC UNIVERSITY OF THE PHILIPPINES OFFICE OF THE VICE PRESIDENT FOR BRANCHES BATAAN BRANCH COURSE TITLE : STATISTICAL ANALYSIS FOR IE 2 COURSE CODE : INEN 201 COURSE CREDIT...

Republic of the Philippines POLYTECHNIC UNIVERSITY OF THE PHILIPPINES OFFICE OF THE VICE PRESIDENT FOR BRANCHES BATAAN BRANCH COURSE TITLE : STATISTICAL ANALYSIS FOR IE 2 COURSE CODE : INEN 201 COURSE CREDIT : 3 units /3 hours Lecture PRE-REQUISITES : INEN 104 COURSE DESCRIPTION : The course is intended as a supplementary course for Statistical Analysis for Industrial Engineering 1. The topics covered for this course are hypothesis testing, design of experiments, correlation, regression and ANOVA. The purpose of this module is to provide a clear presentation of the concepts, principles, tools, and applications of Inferential Statistics and its applications on the field of Industrial Engineering. COURSE OUTCOMES: At the end of the semester, the students should be able to: KNOWLEDGE 1. Know the decision-making process through statistical hypothesis testing. 2. Acquire understanding of statistical treatments using correlation, regression and Analysis of Variance and draw conclusions from these tests. SKILLS 1. Learn to apply the different tools in Statistics and its problem-solving techniques. 2. Demonstrate how to design an experiment and prepare recommendations based on that. VALUE 1. Learn creativity and innovativeness in solving engineering problems using Statistics. 2. Practice discipline and competence in utilizing different statistical tools to arrive in an informed decision. COURSE OUTLINE: Module 1 - Hypothesis Testing Module 2 - Sampling and Design of Experiments Module 3 - Methods Used in Hypothesis Testing Module 4 - Parametric Tests Module 5 - Non- Parametric Tests PREPARED BY : Ma. Celina P. Guanzon Page |1  Republic of the Philippines POLYTECHNIC UNIVERSITY OF THE PHILIPPINES OFFICE OF THE VICE PRESIDENT FOR BRANCHES BATAAN BRANCH MODULE 1 - HYPOTHESIS TESTING Course Objectives: Introduce the students to the concepts and different terminologies in inferential statistics. Familiarize the students with hypotheses testing and its components Demonstrate the different methods to use in hypothesis testing to arrive at a conclusion. Overview : A parameter can be estimated from sample data either by a single number (a point estimate) or an entire interval of plausible values (a confidence interval). Frequently, however, the objective of an investigation is not to estimate a parameter but to decide which of two contradictory claims about the parameter is correct. Methods for accomplishing this comprise the part of statistical inference called hypothesis testing. This module discusses some of the basic concepts and terminology in hypothesis testing and then develops decision procedures for the most frequently encountered testing problems based on a sample from a single population. Course Materials: Statistical Inference: Statistical inference refers to the process of selecting and using a sample statistic to draw conclusions about the population parameter. Statistical inference deals with two types of problems. They are:- 1. Testing of Hypothesis- test a hypothesis or claim about a population parameter 2. Estimation- using sample data to estimate a population parameter Rare Event Rule for Inferential Statistics If, under a given assumption, the probability of a particular observed event is exceptionally small, we conclude that the assumption is probably not correct. Following this rule, we test a claim by analyzing sample data in an attempt to distinguish between results that can easily occur by chance and results that are highly unlikely to occur by chance. We can explain the occurrence of highly unlikely results by saying that either a rare event has indeed occurred or that the underlying assumption is not true. PREPARED BY : Ma. Celina P. Guanzon Page |2  Republic of the Philippines POLYTECHNIC UNIVERSITY OF THE PHILIPPINES OFFICE OF THE VICE PRESIDENT FOR BRANCHES BATAAN BRANCH Hypothesis: A statistical hypothesis, or just hypothesis, is a conjecture, claim or assertion either about the value of a single parameter (population characteristic or characteristic of a probability distribution), about the values of several parameters, or about the form of an entire probability distribution. A statistical hypothesis is a about a population parameter. This conjecture may or may not be true. It is a statement subject to verification, the validity of which remains to be tested. Here are examples of hypotheses : Business. A newspaper headline makes the claim that most workers get their jobs through networking. Medicine. Medical researchers claim that the mean body temperature of healthy adults is not equal to 98.6°F. Aircraft Safety. The Federal Aviation Administration claims that the mean weight of an airline passenger (with carry-on baggage) is greater than the 185 lb that it was 20 years ago. Quality Control. When new equipment is used to manufacture aircraft altimeters, the new altimeters are better because the variation in the errors is reduced so that the readings are more consistent. (In many industries, the quality of goods and services can often be improved by reducing variation.) Hypotheses concerning parameters such as means and proportions can be investigated. There are two specific statistical tests used for hypotheses concerning means: the z test and the t test. The three methods used to test hypotheses are 1. The traditional method 2. The P-value method 3. The confidence interval method The traditional method will be explained first. It has been used since the hypothesis testing method was formulated. A newer method, called the P-value method, has become popular with the advent of modern computers and high-powered statistical calculators. Components of a Formal Hypothesis Test There are two types of statistical hypotheses for each situation: the null hypothesis and the alternative hypothesis. The null hypothesis, symbolized by H0, is a statistical hypothesis that states that there is no difference between a parameter and a specific value, or that there is no difference between two parameters. PREPARED BY : Ma. Celina P. Guanzon Page |3  Republic of the Philippines POLYTECHNIC UNIVERSITY OF THE PHILIPPINES OFFICE OF THE VICE PRESIDENT FOR BRANCHES BATAAN BRANCH Null hypothesis is the original hypothesis. It states that there is no significant difference between the sample and population regarding a particular matter under consideration. The word “null” means ‘invalid’ of ‘void’ or ‘amounting to nothing’. Null hypothesis is denoted by Ho. For example, suppose we want to test whether a medicine is effective in curing cancer. Hence, the null hypothesis will be stated as follows:- H0: The medicine is not effective in curing cancer (i.e., there is no significant difference between the given medicine and other medicines in curing cancer disease.) The alternative hypothesis, symbolized by H1 or Ha, is a statistical hypothesis that states the existence of a difference between a parameter and a specific value, or states that there is a difference between two parameters. Any hypothesis other than null hypothesis is called alternative hypothesis. When a null hypothesis is rejected, we accept the other hypothesis, known as alternative hypothesis. Alternative hypothesis is denoted by H1 or Ha. In the above example, the alternative hypothesis may be stated as follows:- H1: The medicine is effective in curing cancer. (i.e., there is a significant difference between the given medicine and other medicines in curing cancer disease.) The null hypothesis, denoted by H0, is the claim that is initially assumed to be true (the “prior belief” claim). The alternative hypothesis, denoted by Ha or H1, is the assertion that is contradictory to H0. The null hypothesis will be rejected in favor of the alternative hypothesis only if sample evidence suggests that H0 is false. If the sample does not strongly contradict H0, we will continue to believe in the plausibility of the null hypothesis. The two possible conclusions from a hypothesis-testing analysis are then reject H0 or fail to reject H0. PREPARED BY : Ma. Celina P. Guanzon Page |4  Republic of the Philippines POLYTECHNIC UNIVERSITY OF THE PHILIPPINES OFFICE OF THE VICE PRESIDENT FOR BRANCHES BATAAN BRANCH Note About Identifying H0 and H1: Figure 8-2 summarizes the procedures for identifying the null and alternative hypotheses. Note that the original statement could become the null hypothesis, it could become the alternative hypothesis, or it might not correspond exactly to either the null hypothesis or the alternative hypothesis. For example, we sometimes test the validity of someone else’s claim, such as the claim of the Coca-Cola Bottling Company that “the mean amount of Coke in cans is at least 12 oz.” That claim can be expressed in symbols as µ ≥ 12. In Figure 8-2 we see that if that original claim is false, then µ < 12. The alternative hypothesis becomes then µ < 12, but the null hypothesis is then µ = 12. We will be able to address the original claim after determining whether there is sufficient evidence to reject the null hypothesis of µ = 12. EXAMPLE Identifying the Null and Alternative Hypotheses Refer to Figure 8-2 and use the given claims to express the corresponding null and alternative hypotheses in symbolic form. a. The proportion of workers who get jobs through networking is greater than 0.5. b. The mean weight of airline passengers with carry-on baggage is at most 195 lb (the current figure used by the Federal Aviation Administration). c. The standard deviation of IQ scores of actors is equal to 15. SOLUTION See Figure 8-2, which shows the three-step procedure. PREPARED BY : Ma. Celina P. Guanzon Page |5  Republic of the Philippines POLYTECHNIC UNIVERSITY OF THE PHILIPPINES OFFICE OF THE VICE PRESIDENT FOR BRANCHES BATAAN BRANCH a. In Step 1 of Figure 8-2, we express the given claim as p > 0.5. In Step 2 we see that if p >0.5 is false, then p ≤ 0.5 must be true. In Step 3, we see that the expression p > 0.5 does not contain equality, so we let the alternative hypothesis H1 be p > 0.5, and we let H0 be p = 0.5. b. In Step 1 of Figure 8-2, we express “a mean of at most 195 lb” in symbols as µ ≤ 195. In Step 2 we see that if µ ≤ 195 is false, then µ > 195 must be true. In Step 3, we see that the expression µ > 195 does not contain equality, so we let the alternative hypothesis H1 be µ > 195 and we let H0 be µ = 195. c. In Step 1 of Figure 8-2, we express the given claim as δ = 15. In Step 2 we see that if δ = 15 is false, then δ ≠ 15 must be true. In Step 3, we let the alternative hypothesis H1 be δ ≠ 15, and we let H0 be δ = 15. Testing of Hypothesis: Testing of hypothesis is a process of examining whether the hypothesis formulated by the researcher is valid or not. The main objective of hypothesis testing is whether to accept or reject the hypothesis. Hypothesis testing, which is a decision-making process for evaluating claims about a population. In hypothesis testing, the researcher must define the population under study, state the particular hypotheses that will be investigated, give the significance level, select a sample from the population, collect the data, perform the calculations required for the statistical test, and reach a conclusion. PREPARED BY : Ma. Celina P. Guanzon Page |6  Republic of the Philippines POLYTECHNIC UNIVERSITY OF THE PHILIPPINES OFFICE OF THE VICE PRESIDENT FOR BRANCHES BATAAN BRANCH A statistical hypothesis, or just hypothesis, is a claim or assertion either about the value of a single parameter (population characteristic or characteristic of a probability distribution), about the values of several parameters, or about the form of an entire probability distribution. One example of a hypothesis is the claim µ=.75, where µ is the true average inside diameter of a certain type of PVC pipe. Another example is the statement p <.10 , where p is the proportion of defective circuit boards among all circuit boards produced by a certain manufacturer. If µ1 and µ2 denote the true average breaking strengths of two different types of twine, one hypothesis is the assertion that µ1- µ2 = 0, and another is the statement that µ1- µ2 > 5. Yet another example of a hypothesis is the assertion that the stopping distance under particular conditions has a normal distribution. In any hypothesis-testing problem, there are two contradictory hypotheses under consideration. One hypothesis might be the claim µ = 5.75 and the other µ ≠ 5.75, or the two contradictory statements might be p ≥.10 and p <.10. The objective is to decide, based on sample information, which of the two hypotheses is correct. There is a familiar analogy to this in a criminal trial. One claim is the assertion that the accused individual is innocent. In the U.S. judicial system, this is the claim that is initially believed to be true. Only in the face of strong evidence to the contrary should the jury reject this claim in favor of the alternative assertion that the accused is guilty. In this sense, the claim of innocence is the favored or protected hypothesis, and the burden of proof is placed on those who believe in the alternative claim. Similarly, in testing statistical hypotheses, the problem will be formulated so that one of the claims is initially favored. This initially favored claim will not be rejected in favor of the alternative claim unless sample evidence contradicts it and provides strong support for the alternative assertion. A test of hypotheses is a method for using sample data to decide whether the null hypothesis should be rejected. Thus we might test H0: µ =.75 against the alternative Ha: µ ≠.75. Only if sample data strongly suggests that µ is something other than.75 should the null hypothesis be rejected. In the absence of such evidence, H0 should not be rejected, since it is still quite plausible. Sometimes an investigator does not want to accept a particular assertion unless and until data can provide strong support for the assertion. As an example, suppose a company is considering putting a new type of coating on bearings that it produces. The true average wear life with the current coating is known to be 1000 hours. With µ denoting the true average life for the new coating, the company would not want to make a change unless evidence strongly suggested that µ exceeds 1000. An appropriate problem formulation would involve testing against Ha: µ > 1000. The conclusion that a change is justified is identified with Ha, and it would take conclusive evidence to justify rejecting H0 and switching to the new coating. Scientific research often involves trying to decide whether a current theory should be replaced by a more plausible and satisfactory explanation of the phenomenon under investigation. A conservative approach is to identify the current theory with H0 and the researcher’s alternative explanation with Ha. Rejection of the current theory will then occur only when evidence is much PREPARED BY : Ma. Celina P. Guanzon Page |7  Republic of the Philippines POLYTECHNIC UNIVERSITY OF THE PHILIPPINES OFFICE OF THE VICE PRESIDENT FOR BRANCHES BATAAN BRANCH more consistent with the new theory. In many situations, Ha is referred to as the “researcher’s hypothesis,” since it is the claim that the researcher would really like to validate. The word null means “of no value, effect, or consequence,” which suggests that H0 should be identified with the hypothesis of no change (from current opinion), no difference, no improvement, and so on. Suppose, for example, that 10% of all circuit boards produced by a certain manufacturer during a recent period were defective. An engineer has suggested a change in the production process in the belief that it will result in a reduced defective rate. Let p denote the true proportion of defective boards resulting from the changed process. Then the research hypothesis, on which the burden of proof is placed, is the assertion that p <.10. Thus the alternative hypothesis is Ha: p <.10. In our treatment of hypothesis testing, H0 will generally be stated as an equality claim. If 𝜃 denotes the parameter of interest, the null hypothesis will have the form H0: θ = θ0, where θ0 is a specified number called the null value of the parameter (value claimed for θ by the null hypothesis). As an example, consider the circuit board situation just discussed. The suggested alternative hypothesis was Ha: p <.10 , the claim that the defective rate is reduced by the process modification. A natural choice of H0 in this situation is the claim that p ≥.10, according to which the new process is either no better or worse than the one currently used. We will instead consider H0: p =.10 versus Ha: p θ0, (in which case the implicit null hypothesis is θ ≤ θ0 ), 2. Ha: θ < θ0, (in which case the implicit null hypothesis is θ ≥ θ0 ), or 3. Ha: θ ≠ θ0 For example, let δ denote the standard deviation of the distribution of inside diameters (inches) for a certain type of metal sleeve. If the decision was made to use the sleeve unless sample evidence conclusively demonstrated that δ >.001, the appropriate hypotheses would be H0: δ =.001 versus Ha: δ >.001. The number θ0 that appears in both H0 and Ha (separates the alternative from the null) is called the null value. Procedure for Testing of Hypothesis: A test procedure is specified by the following: 1. A test statistic, a function of the sample data on which the decision (reject H0 or do not reject H0) is to be based 2. A rejection region, the set of all test statistic values for which H0 will be rejected The null hypothesis will then be rejected if and only if the observed or computed test statistic value falls in the rejection region. The various steps in testing of hypothesis involves the following :- PREPARED BY : Ma. Celina P. Guanzon Page |8  Republic of the Philippines POLYTECHNIC UNIVERSITY OF THE PHILIPPINES OFFICE OF THE VICE PRESIDENT FOR BRANCHES BATAAN BRANCH 1. Set Up a Hypothesis: The first step in testing of hypothesis is to set p a hypothesis about population parameter. Normally, the researcher has to fix two types of hypotheses. They are null hypothesis and alternative hypothesis. 2. Set up a suitable level of significance: After setting up the hypothesis, the researcher has to set up a suitable level of significance. The level of significance is the probability with which we may reject a null hypothesis when it is true. For example, if the level of significance is 5%, it means that in the long run, the researcher is rejecting true null hypothesis 5 times out of every 100 times. Level of significance is denoted by α (alpha). α = Probability of rejecting H0 when it is true. Generally, the level of significance is fixed at 1% or 5%. 3. Decide a test criterion: The third step in testing of hypothesis is to select an appropriate test criterion. Commonly used tests are z-test, t-test, X2 – test, F-test, etc. 4. Calculation of test statistic: The next step is to calculate the value of the test statistic using appropriate formula. The general form for computing the value of test statistic is:- Value of Test statistic = Difference Standard Error 5. Making Decision: Finally, we may draw conclusions and take decisions. The decision may be either to accept or reject the null hypothesis. If the calculated value is more than the table value, we reject the null hypothesis and accept the alternative hypothesis. If the calculated value is less than the table value, we accept the null hypothesis. A statistical test uses the data obtained from a sample to make a decision about whether the null hypothesis should be rejected. The numerical value obtained from a statistical test is called the test value. In this type of statistical test, the mean is computed for the data obtained from the sample and is compared with the population mean. Then a decision is made to reject or not reject the null PREPARED BY : Ma. Celina P. Guanzon Page |9  Republic of the Philippines POLYTECHNIC UNIVERSITY OF THE PHILIPPINES OFFICE OF THE VICE PRESIDENT FOR BRANCHES BATAAN BRANCH hypothesis on the basis of the value obtained from the statistical test. If the difference is significant, the null hypothesis is rejected. If it is not, then the null hypothesis is not rejected. In the hypothesis-testing situation, there are four possible outcomes. In reality, the null hypothesis may or may not be true, and a decision is made to reject or not reject it on the basis of the data obtained from a sample. The four possible outcomes are shown in Figure 8–2. Notice that there are two possibilities for a correct decision and two possibilities for an incorrect decision. If a null hypothesis is true and it is rejected, then a type I error is made. In situation A, for instance, the medication might not significantly change the pulse rate of all the users in the population; but it might change the rate, by chance, of the subjects in the sample. In this case, the researcher will reject the null hypothesis when it is really true, thus committing a type I error. On the other hand, the medication might not change the pulse rate of the subjects in the sample, but when it is given to the general population, it might cause a significant increase or decrease in the pulse rate of users. The researcher, on the basis of the data obtained from the sample, will not reject the null hypothesis, thus committing a type II error. In situation B, the additive might not significantly increase the lifetimes of automobile batteries in the population, but it might increase the lifetimes of the batteries in the sample. In this case, the null hypothesis would be rejected when it was really true. This would be a type I error. On the other hand, the additive might not work on the batteries selected for the sample, but if it were to be used in the general population of batteries, it might significantly increase their lifetimes. The researcher, on the basis of information obtained from the sample, would not reject the null hypothesis, thus committing a type II error. PREPARED BY : Ma. Celina P. Guanzon P a g e | 10  Republic of the Philippines POLYTECHNIC UNIVERSITY OF THE PHILIPPINES OFFICE OF THE VICE PRESIDENT FOR BRANCHES BATAAN BRANCH A type I error occurs if you reject the null hypothesis when it is true. A type II error occurs if you do not reject the null hypothesis when it is false. The hypothesis-testing situation can be likened to a jury trial. In a jury trial, there are four possible outcomes. The defendant is either guilty or innocent, and he or she will be convicted or acquitted. See Figure 8–3. Now the hypotheses are H0: The defendant is innocent H1: The defendant is not innocent (i.e., guilty) Next, the evidence is presented in court by the prosecutor, and based on this evidence, the jury decides the verdict, innocent or guilty. If the defendant is convicted but he or she did not commit the crime, then a type I error has been committed. See block 1 of Figure 8–3. On the other hand, if the defendant is convicted and he or she has committed the crime, then a correct decision has been made. See block 2. If the defendant is acquitted and he or she did not commit the crime, a correct decision has been made by the jury. See block 3. However, if the defendant is acquitted and he or she did commit the crime, then a type II error has been made. See block 4. The decision of the jury does not prove that the defendant did or did not commit the crime. The decision is based on the evidence presented. If the evidence is strong enough, the defendant will be convicted in most cases. If the evidence is weak, the defendant will be acquitted in most cases. Nothing is proved absolutely. Likewise, the decision to reject or not reject the null hypothesis does not prove anything. The only way to prove anything statistically is to use the entire population, which, in most cases, is not possible. The decision, then, is made on the basis of probabilities. That is, when there is a large difference between the mean obtained from the sample and the hypothesized mean, the null hypothesis is probably not true. The question is, how large a difference is necessary to reject the null hypothesis? Here is where the level of significance is used. The level of significance is the maximum probability of committing a type I error. This probability is symbolized by a (Greek letter alpha). That is, P(type I error)= α. The probability of a type II error is symbolized by β, the Greek letter beta. That is, P(type II error)= β. In most hypothesis-testing situations, β cannot be easily computed; however, α and β are related in that decreasing one increases the other. Statisticians generally agree on using three arbitrary significance levels: the 0.10, 0.05, and 0.01 levels. That is, if the null hypothesis is rejected, the probability of a type I error will be 10%, 5%, or 1%, depending on which level of significance is used. Here is another way of putting PREPARED BY : Ma. Celina P. Guanzon P a g e | 11  Republic of the Philippines POLYTECHNIC UNIVERSITY OF THE PHILIPPINES OFFICE OF THE VICE PRESIDENT FOR BRANCHES BATAAN BRANCH it: When α = 0.10, there is a 10% chance of rejecting a true null hypothesis; when α = 0.05, there is a 5% chance of rejecting a true null hypothesis; and when α = 0.01, there is a 1% chance of rejecting a true null hypothesis. In a hypothesis-testing situation, the researcher decides what level of significance to use. It does not have to be the 0.10, 0.05, or 0.01 level. It can be any level, depending on the seriousness of the type I error. After a significance level is chosen, a critical value is selected from a table for the appropriate test. If a z test is used, for example, the z table is consulted to find the critical value. The critical value determines the critical and noncritical regions. The critical value can be on the right side of the mean or on the left side of the mean for a one-tailed test. Its location depends on the inequality sign of the alternative hypothesis. For example, in situation B, where the chemist is interested in increasing the average lifetime of automobile batteries, the alternative hypothesis is H1: µ > 36. Since the inequality sign is >, the null hypothesis will be rejected only when the sample mean is significantly greater than 36. Hence, the critical value must be on the right side of the mean. Therefore, this test is called a right-tailed test. PREPARED BY : Ma. Celina P. Guanzon P a g e | 12 Republic of the Philippines POLYTECHNIC UNIVERSITY OF THE PHILIPPINES OFFICE OF THE VICE PRESIDENT FOR BRANCHES BATAAN BRANCH PREPARED BY : Ma. Celina P. Guanzon P a g e | 13 Republic of the Philippines POLYTECHNIC UNIVERSITY OF THE PHILIPPINES OFFICE OF THE VICE PRESIDENT FOR BRANCHES BATAAN BRANCH PREPARED BY : Ma. Celina P. Guanzon P a g e | 14 Republic of the Philippines POLYTECHNIC UNIVERSITY OF THE PHILIPPINES OFFICE OF THE VICE PRESIDENT FOR BRANCHES BATAAN BRANCH PREPARED BY : Ma. Celina P. Guanzon P a g e | 15 Republic of the Philippines POLYTECHNIC UNIVERSITY OF THE PHILIPPINES OFFICE OF THE VICE PRESIDENT FOR BRANCHES BATAAN BRANCH PREPARED BY : Ma. Celina P. Guanzon P a g e | 16  Republic of the Philippines POLYTECHNIC UNIVERSITY OF THE PHILIPPINES OFFICE OF THE VICE PRESIDENT FOR BRANCHES BATAAN BRANCH TEST STATISTIC The decision to accept or to reject a null hypothesis is made on the basis of a statistic computed from the sample. Such a statistic is called the test statistic. There are different types of test statistics. All these test statistics can be classified into two groups. They are a. Parametric Tests b. Non-Parametric Tests PARAMETRIC TESTS The statistical tests based on the assumption that population or population parameter is normally distributed are called parametric tests. The important parametric tests are:- 1. z-test – z-test is applied when the test statistic follows normal distribution. It was developed by Prof. R. A. Fisher. 2. t-test - t-distribution was originated by W.S. Gosset in the early 1900s. t-test is applied when the test statistic follows t-distribution. 3. f-test - F-test is used to determine whether two independent estimates of population variance significantly differ or to establish both have come from the same population. For carrying out the test of significance, we calculate a ration, called F-ratio. F-test is named in honor of the great statistician R. A. Fisher. It is also called Variance Ration Test. PREPARED BY : Ma. Celina P. Guanzon P a g e | 17 Republic of the Philippines POLYTECHNIC UNIVERSITY OF THE PHILIPPINES OFFICE OF THE VICE PRESIDENT FOR BRANCHES BATAAN BRANCH PREPARED BY : Ma. Celina P. Guanzon P a g e | 18  Republic of the Philippines POLYTECHNIC UNIVERSITY OF THE PHILIPPINES OFFICE OF THE VICE PRESIDENT FOR BRANCHES BATAAN BRANCH Decision Criterion. The decision to reject or fail to reject the null hypothesis is usually made using either the traditional method (or classical method) of testing hypotheses, the P-value method, or the decision is sometimes based on confidence intervals. In recent years, use of the P-value method has been increasing along with the inclusion of P-values in results from software packages. PREPARED BY : Ma. Celina P. Guanzon P a g e | 19  Republic of the Philippines POLYTECHNIC UNIVERSITY OF THE PHILIPPINES OFFICE OF THE VICE PRESIDENT FOR BRANCHES BATAAN BRANCH Wording the Final Conclusion. The conclusion of rejecting the null hypothesis or failing to reject it is fine for those of us with the wisdom to take a statistics course, but we should use simple, nontechnical terms in stating what the conclusion really means. Figure 8-7 summarizes a procedure for wording of the final conclusion. Note that only one case leads to wording indicating that the sample data actually support the conclusion. If you want to support some claim, state it in such a way that it becomes the alternative hypothesis, and then hope that the null hypothesis gets rejected. Accept Fail to Reject. Some texts say, “accept the null hypothesis” instead of “fail to reject the null hypothesis.” Whether we use the term accept or fail to reject, we should recognize that we are not proving the null hypothesis; we are merely saying that the sample evidence is not strong PREPARED BY : Ma. Celina P. Guanzon P a g e | 20  Republic of the Philippines POLYTECHNIC UNIVERSITY OF THE PHILIPPINES OFFICE OF THE VICE PRESIDENT FOR BRANCHES BATAAN BRANCH enough to warrant rejection of the null hypothesis. (When a jury does not find enough evidence to convict a suspect, it returns a verdict of not guilty; it does not return a verdict of innocence.) The term accept is somewhat misleading, because it seems to imply incorrectly that the null hypothesis has been proved. (It is misleading to state that “there is sufficient evidence to accept correctly that the available evidence isn’t strong enough to warrant rejection of the null hypothesis. In this text we will use the terminology fail to reject the null hypothesis, instead of accept the null hypothesis. PREPARED BY : Ma. Celina P. Guanzon P a g e | 21  Republic of the Philippines POLYTECHNIC UNIVERSITY OF THE PHILIPPINES OFFICE OF THE VICE PRESIDENT FOR BRANCHES BATAAN BRANCH REFERENCES To understand more about hypothesis testing, browse through the following references: LIBRARY REFERENCES 1. QA 273.B33; Baccay, Elisa S.; Statistics and Probability 2022 2. QA 276.12.C66; Coolidge, Frederick L.; Statistics : A Gentle Introduction 2021 3. e-book; Durivage, Mark Allen; Practical Engineering, Process, and Reliability Statistics 2022 OTHER REFERENCES 1. JAY DEVORE, Probability and Statistics for Engineering and the Sciences; 8th edition, Copyright 2010 Cengage Learning. All Rights Reserved. ISBN-13: 978-0-538-73352-6, ISBN-10: 0-538-73352-7 2. Allan G. Bluman; ELEMENTARY STATISTICS: A STEP BY STEP APPROACH, SEVENTH EDITION, Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas, New York, NY 10020. Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved. Previouseditions © 2007, 2004, 2001, 1998, and 1995. 3. Triola, Mario F.; Elementary statistics, 10th edition, Copyright © 2006 Pearson Education, 75 Arlington Street, Suite 300, Boston, MA 02116. All rights reserved. ISBN 0-321-33183- 4 PREPARED BY : Ma. Celina P. Guanzon P a g e | 22  Republic of the Philippines POLYTECHNIC UNIVERSITY OF THE PHILIPPINES OFFICE OF THE VICE PRESIDENT FOR BRANCHES BATAAN BRANCH ACTIVITIES/ASSESSMENTS A. Answer the following: I. Statistical Literacy and Critical Thinking 1. Proving That p 5 0.5 A newspaper article states that “based on a recent survey, it has been proved that 50% of all truck drivers smoke.” What is wrong with that statement? 2. Null Hypothesis The quality control manager of a cola bottling company claims that “the mean amount of cola in our cans is at least 12 ounces.” In testing that claim, express the null hypothesis and alternative hypothesis in symbolic form. Does the original claim correspond to the null hypothesis, alternative hypothesis, or neither? 3. Test Statistic and Critical Value What is the difference between a test statistic and a critical value? 4. P-Value You have developed a new drug, and you claim that it lowers cholesterol, so you express the claim as m , 100 (where 100 is a standardized index of cholesterol). Which P-value would you prefer to get: 0.04 or 0.01? Why? II. Identifying H0 and H1. Examine the given statement, then express the null hypothesis H0 and alternative hypothesis H1 in symbolic form. Be sure to use the correct symbol (µ, p, δ) for the indicated parameter. 5. More than 25% of Internet users pay bills online. 6. Most households have telephones. 7. The mean weight of women who won Miss America titles is equal to 121 lb. 8. The mean top of knee height of a sitting male is 20.7 in. 9. IQ scores of college professors have a standard deviation less than 15, which is the standard deviation for the general population. 10. High school teachers have incomes with a standard deviation that is less than $20,000. 11. Plain M&M candies have a mean weight that is at least 0.8535 g. 12. The percentage of workers who got a job through their college is no more than 2%. Format: Font- Calibri, size -12, spacing- double, each paragraph indented; copy the questions only in italics before answering. Your answers from this assessments/activity shall be uploaded on your Google Classroom on the prescribed date and time of submission. PREPARED BY : Ma. Celina P. Guanzon P a g e | 23