Null Hypothesis And Alternative Hypothesis Philosophy Essay

Null supposition And Alternative Hypothesis Philosophy EssayIn order to survive in the business world, business wholes today are forced to innovate and launch the merchandises immediately in the foodstuff. But this is easier said than done. Numerous factors come into the picture for this to materialise. nonably among them is the fact that too much cost factor which comes into the picture. For the harvest-home launching is well planned and thought off activity.The activities include apportioning market surveys which in seemingly sense means that the business units are required to conduct or determine the feasibility of the new product deep down a limited reach and then found on the results they bear away further course of action i.e. go ahead with the launch of the product or to drop the project altogether.In other words, business units conduct type surveys i.e. obtaining the response on a piddling piece of the larger picture and then found on the results of the small piece, estimate the likely response on the larger piece of the picture. The small piece is known as the sample and the larger piece is known as the universe of discourse. thence the concept of sample and universe plays a vital role and assists the management in taking core decisions which may or non shew fruitful in the survival of the business. In order, to take decisions based on the sample and to estimate the population arguings business units are required to start with about of the habituateds or the assumption. And, based on assumptions or supposition about the population it is mental block outed meaning that whatever the assumption that they started with, whether the assumption was correct or incorrect. Thus we have opening testing.Let us take an example to illustrate what has been said higher up. reckon, the business units want to bring in a new product in the market which leave alone increase the market share and hence the profitability of the business unit. In this circumstance, the possibility would be introduction of new product will increase the profitability and based on this the survey would be conducted. The results of analysis of the entropy will reveal whether the conjecture was correct or incorrect.This unit will cover the basics of guessing and its testing the step required to test the possibility. This unit will also cover the types and characteristics of system and the like.ObjectivesAfter canvas this unit, the reader will be able toUnderstand the basic concepts of assumptionUnderstand the mingled types and the characteristics of hypothesisUnderstand the steps involved in the testing of hypothesisUnderstand the deuce tailed and the one tailed tests involved in the testing of hypothesisUnderstand the criterion when to get into or when to eliminate the hypothesisUnderstand the manner in which decisions are to be taken on the basis of the results arrived during the process of testing of hypothesis6.2 Defining Hyp othesisIn order to discuss the basics of hypothesis testing in detail concede us now, define what is meant by hypothesis.Simply speaking, hypothesis is a unit of the inferential statistics (i.e. the branch of statistics which is employ to infer in take ination on the collected data) which is used to test a claim about the larger portion (which is called population) based on the data collected from the smaller part known as sample. In other words hypothesis testing is the process of staking claim based on the places obtained from the sample.Let us take an example in order to drive home the point illustrated above.A manufacturer involved in the manufacturing of types claims that the average life of their tires will delay at least 70,000 kms. We want to test the claim made by the manufacturer. The process we will adopt is to take a sample of tires, run them until they see how many kms. on average they have lasted. If the sample has lasted over 70,000 kms, then we do have the reaso n to look at that the claim is correct and that all the other tires they produce will also last 70,000 kms. miles.In arriving at this conclusion, we may commit the undermentionedWe may wrong say the tires do not last at least 70,000 kms when in fact they do lastWe may incorrectly say the tires do last at least 70,000 kms when in fact they do notThus, we may commit any(prenominal) errors during the process of staking the claim to the hypothesis we have hypothesise.This aspect will be covered in next sectionSelf Assessment QuestionsTrue or FalseManagers are required to make decisionsHypothesis is an assumption about something which is taken to be trueWe may commit some errors in the process of testing of hypothesis6.3 Characteristics of HypothesisHaving understood the definition of hypothesis, let us now understand the characteristics of hypothesis. The following are the characteristics of hypothesis.A hypothesis is based on reasoning which appears to be justifiedThis simply mean s that the hypothesis we have formulated should be based on the previous explore and the hypothesis should follow the most likely outcome not the exceptional outcome. For example, we should form the hypothesis regarding the launching of new product on the basis of the previous data which was analysed and which prompted us to take further steps such as market research and the likeA hypothesis should provide a reasonable explanation for the outcome which is to be predictedThis means that the hypothesis formulated should not think on the unrealistic outcome i.e. the hypothesis should be based on the realistic scenario. For example, an hypothesis such as our new software will spend the sales of the software dealer who is leading the software market or that our software will sell very(prenominal) well on the surface of the moon. all in all these are unrealistic.A hypothesis should clearly state the kinship between the variables that are definedThis simply means that the hypothesis should not be vague. It should be in plain simple terms and in a language which is simple to understand. For example, the hypothesis that the MIS report will be printed somewhat in 3 to 4 minutes is ambiguous and confusing.A hypothesis defines the variables measurable termsThis means that the hypothesis focus on the aspects such as who all would be affected who are the players in the process and the like. For example, hypothesis, that the product will work correctly for 2 months for small children.A hypothesis is testable in a devoted or satisfactory amount of timeThis means that the hypothesis is tested within a finite amount of time. An hypothesis which cannot be tested within the finite amount of time will never be tested nor acceptedSelf Assessment QuestionsFill in the blanksA hypothesis is _________ in a given period of ______________Hypothesis defines __________ in measurable termsHypothesis should define the ________ between the variables6.4 geeks of HypothesisHaving under stood the basic terminology of hypothesis let us now discuss the types of hypothesis. Though we have just scratched the types of hypothesis, let us now go deeper into the detail of types of hypothesis.Hypothesis are of various types. Some of them are discussed belowNull hypothesisAlternate hypothesisSimple HypothesisComplex hypothesisNull HypothesisThis hypothesis is formulated when the statistician believes that thither is no relationship between dickens variables or when at that place is insufficient information to formulate a state a research hypothesis. It is denoted by H0Alternate hypothesisThis hypothesis is the opposite of Null hypothesis. it is formulated then the researcher believes that there is sufficient information to believe that there is relationship between the variables. It is represented as H1 or HSimple hypothesisThis hypothesis predicts the relationship between an independent variable and a dependent variable. both the variables must be single variables Complex hypothesisThis hypothesis is used to predict the relationship between two or more independent variables and two or more dependent variables manikins of different types of HypothesisHealth related education programmes influence the number of people who smokeNewspapers affects peoples living standardAbsenteeism in classes affects exam scoresLower levels of exercise is responsible for increase in weightSelf Assessment QuestionsTrue or FalseComplex hypothesis is used to predict the relationship between two or more independent variable with two or more dependent variablesAlternate hypothesis is opposite to empty hypothesis6.5 Hypothesis TestingHaving understood the various types of hypothesis let us dwell on the important point of hypothesis testing. As stated above hypothesis means that we verify the claim on the larger unit based on the data and the results obtained by do statistical tests on the data. let us now look at the steps involved in the testing of hypothesis. the following are the steps hear in a statement about the population characteristic for which the hypotheses is to be tested deposit the null hypothesis and depict as HoState the alternative hypothesis depict it as H1 or HaIdentify and display the test statistic that will be usedIdentify the sphere of rejection regionIs it on the upper, lower, or on the two-tailed testDetermine the critical value that will be associated as a, the level of significance at which the test is to be conductedCompute the quantities in the test statisticState the conclusion based on the computed statistics meaning that it is now to be decided as to whether reject the null hypothesis, Ho, or accept the alternate hypothesis. The conclusion is dependent on the level of significance of the test.Figure 1 provides a graphical view of the steps involved in the testing of hypothesisFigure 1 Steps involved in the testing of hypothesis6.6 Difference between Null Hypothesis and Alternative HypothesisIn the previous units we hav e understood the basics of null hypothesis and alternative hypothesis, let us now discuss the difference between these types of hypothesis. the following are the differencesNull hypothesis is used to describe the prediction while alternative hypothesis describes other possible outcomes. For example, if we predict A is related to B which is null hypothesis while the alternative hypothesis will be A is not related to B meaning that A can be teacher of B, A can be mentor of B and so onThe alternative hypothesis can be negative but it does not necessarily mean a negation of null hypothesis but rather that it is a measure of finding out whether the null hypothesis is true or not meaning that whether it should be accepted or it should be rejectedAlternative hypothesis provides an opportunity to look at other things and other possibilities where as null hypothesis provides the presence or absence of the same meaning that when we deal with null hypothesis our focus becomes restricted while in the case of alternative hypothesis our focus needs to be wider6.7 Decision RuleDecision rules are the procedures that enable us to determine whether the findings of the observed samples are in sharp contradiction i.e. there is large difference from the results that were expected and which will thus help us to decide whether to accept or reject hypotheses are called rules of decision or simply decision rules.Let us take an example in order to illustrate what has been said with regard to decision rule. cypher that we toss a coin 50 times and get head 42 times and if we had the null hypothesis that the coir is fair. Now in this scenario, there is sufficient reason to believe that the coin is biased based on the output obtained although we may be wrong in this manner. In the current scenario, the observations are verbalize something else in comparison to our hypothesis, hence, we are in a dilemma as to accept or reject the hypothesis. Procedures , which assist us in deciding wheth er to accept or reject the hypothesis when there is significant difference between the observed and the stated are know an Decision Rules. figure I and Type II errorsIt is in situations like the above, that we may commit errors or mistakes which are classified asType I or Type II errors.Type I error is when we reject the hypothesis when it should have been acceptedType II error is when we accept a hypothesis when it should have been rejectedFrom the above definitions, in both the cases a wrong decision has been made. Hence, it becomes imperative that we need to minimize the errors while making decisions.Level of SignificanceWhile testing the given hypothesis the maximum risk that we can take for Type I error is called the level of signicance of the test. This is denoted by Greek letter Alpha . It is decided earlier hand so that they do not influence the choice of our decisions.6.8 Two tailed and one tailed testsIn order to understand the concept of two tailed and one tailed tests, consider the following scenario. Let us have a null hypothesis H0and an alternative hypothesis H1. We want to conduct the test and determine whether we should reject the null hypothesis in privilege of alternative hypothesis.Thus, we have two different types of test which can be performed videlicet One Tailed test and Two Tailed testOne-tailedtest seeks to look for an increase or decrease in the parameter under context while two-tailedtest seeks to look for any change in the parameterWe can carry out the test at any level 1%, 5% or 10% are the common levels. For example, when we perform the test at a 5% level it means that there is a 5% chance of wrongly rejecting H0 that is null hypothesis on the other hand If we perform the test at the 5% level and decide to reject the null hypothesis, we say that there is a significant evidence at 5% to suggest that the hypothesis is false.One-Tailed TestFor the one tailed test we choose a critical region. In a one-tailed test, the critical re gion will have one part. If the sample value lies in this region, we will reject the null hypothesis in favour of the alternativeOn the other hand , if we want to look for definite decrease. Then the critical region will be to the left.ExampleSuppose we are given that in aPoisson distributionand we want to test hypothesis on the mean,based upon a sample of observation 3.Suppose the hypotheses areH0l= 9H1lWe want to test if it is reasonable for the value observed to be 3 to have been derived from Poisson distribution with having a parameter value of 9. What is the probability that the value as low as 3 has come from a Poisson distribution have the value 9?P(X 3) = 0.0212 (this has been obtained from Poisson table)The probability is s gently than 0.05, which means that there is less than a 5% chance that the value has come from a Poisson(3) distribution. The null hypothesis should be rejected in favour of the alternative at the 5% level.Two-Tailed TestIn a two-tailed test, we look fo r either an increase or a decrease. Hence, for example, H0might be that the mean is fit to 9 (as before). This time, however, H1would be that the mean is not equal to 9. So, In this case, therefore, the critical region has two partsExampleLets test the parameter p of aBinomial distributionat the 10% level.Suppose a coin is tossed 10 times and we get 7 heads. We want to test whether or not the coin is fair. If the coin is fair, p = 0.5 . Put this as the null hypothesisH0 p = 0.5H1 p 0.5Because this is a 2-tailed test, the critical region also has two parts. half(a) of the critical region is to in the right and other half is in the left. So the critical region contains both the top 5% of the distribution and the backside 5% of the distribution (as we are testing at the 10% level).If H0is true, X Bin(10, 0.5).If the null hypothesis is true, what is the probability that X is 7 or above?P(X 7) = 1 P(X Is this in the critical region? No- because the probability that X is at least 7 is not less than 0.05 (5%), which is what we need it to be.So there is no significant evidence to reject the null hypothesis at 10% level of significance6.9 Procedure of Hypothesis testingHaving understood the basics of hypothesis, let us now dwell on the procedure which is to be followed in the testing of hypothesis. The following are the steps that are to be followed.State null hypothesis and alternative hypothesisState the level of significance. This gives us the tabulated valuesSelect the appropriate testCalculate the required values for the testConduct the testDraw the conclusions6.10 SummaryA hypothesis is necessary in todays business world as the managers are required to take decisions and they need to have a starting pointHypothesis is astray used in the conduct of market surveysThe concept of sample and population is widely used in the testing of hypothesisHypothesis is a unit of inferential statisticsHypothesis is based on reasoning which appears to be justifiedNull hypo thesis is formed when there is n relationship between the variablesAlternative hypothesis is the reverse of null hypothesisDecisions rules provide the basis for accepting the or rejecting the hypothesisType I error is when we reject the hypothesis when it should have been acceptedType II error is when we accept the hypothesis when we should have rejected it6.11 Terminal QuestionsWhat is the significance of hypothesis testing?What is meant by Type I and Type II errors? Explain with examplesWhat is the difference between Null hypothesis and Alternative hypothesis?Explain the steps involved in the testing of hypothesis.6.12 Answers Self Assessment QuestionsTrueFalseTrueTestable TimeVariablesRelationshipTrueTrue6.13 Suggested ReadingBooksTesting statistical hypothesis, Lehmann, JosephHypothesis testing with SPSS, Jim MirabellaFundamentals of Statistics, Michael SullivanFundamentals of Statistics, S.C. GuptaFundamentals of Statistics, Trueman Lee KellyIntroductory Probability And Statist ical Applications, MeyerFundamental of Statistics, Vol II, Goon, Gupta and DaguptaAn Outline of Statistical Theory, Vol I, Goon, Gupta and DaguptaA Basic melodic phrase in Statistics, Clarke, Geoffrey and Cooke, John Wiley SonsBasic Statistics, Nagar DasQuantitative Techniques for Decision Making, Anand SharmaStatistics for economists A beginning, John E. FloydThe Elements of Statistical Learning, Trevor Hastie, Jerome Friedman.Introduction to Statistical Thought, Michael LavineWeb Resourcesen.wikipedia.org/wiki/Statistical_hypothesis_testingwww.slideshare.net/vikramlawand/test-of-hypothesiswww.sagepub.com/upm-data/40007_Chapter8.pdfwww.iasri.res.in/ebook//2/4-TEST%20OF%20HYPOTHESIS.pdfwww.math.uah.edu/stat/hypothesis/index.htmlwww.angelfire.com/wv/bwhomedir/notes/z_and_t_tests.pdfwww.20bits.com/ name/hypothesis-testing-the-basicswww.amstat.org/publications/jse/v11n3/java/Hypothesis/math.bu.edu/people/nkatenka/MA113/Lecture_10_Notes.pdfwww.pstcc.edu/facstaff/jwlamb/Math1530/7.2rv sd.ppt6.14 GlossaryAggregateIt is the collection of small units which results in one complete entity. For example the aggregation of the total inhabitants of towns and villages and mega cities results in the population of the countryAlpha LevelThe probability that the statistical test will find difference between the groups which is significant when there are none. This is also termed as the probability of making a Type I error or as the significance level of statistical test.Alternative HypothesisThe hypothesis that states that there is some difference between two or more groups. It is the alternative to null hypothesis, which states that there is no difference among the groups.Analysis of Variance (ANOVA)A test that determines whether the means of two or more groups is significantly different.AssociationIt is a type of relationship between objects or variables.AverageA single value which may be mean, median or mode and represents the typical, normal, or the middle value of a given set of data.AxiomA statement widely accepted as truth.Bell-Shaped CurveA meander which is the characteristic of a normal distribution, which is symmetrical about the mean. The area under the normal curve is 1.0.Beta LevelIt is the probability of making an error due to the result of the chance variations when in actuality they are due to the differences of the result of the experimental manipulation or intervention. It is also referred to as the probability of making a Type II error.BiasThey are the influences that contribute to the distortions of the resultsCategorical DataThey are also referred to as the nominal data. They are for indicative purpose onlyCausal AnalysisAn analysis that seeks to establish the cause and effect relationships between variables.Central TendencyA measure that describes the central characteristic of the distribution.ComparabilityIt is the quality of two or more entities that are to be evaluated for their similarity and differences.Confidence IntervalA p ersona of estimated values that provides the best estimate regarding the populations values.Confidence LevelIt is the percentage which represents the number of times that a confidence interval will include the true population value.ConsistencyIt is the process in which similar responses are demonstrated throughout the activity / event.ConstantIt is the value which does not changeDescriptive StatisticsIt is the basic statistics that is used to describe and summarize data.Focus GroupAn interview conducted with a small group of people, all at one time, to explore ideas on a occurrence topic.Multivariate AnalysisIt is the analysis of several independent variable on the dependent variable.Mutually ExclusiveIt is when the happening of an event does not disturb or alters the happening of another event. for example, in tossing of coin, the appearance of head is mutually exclusive to the appearance of tail as any one of them say head, does not allow the other to happen simultaneously.Nomina l ScaleIt is a scale that allows for classifying of elements into several mutually exclusive categories which are based on defined features but no numeric. They are just used for identification purposes. For example, the shirts worn by players in a football match. The number on the shirts represent the identification of the player only. prescript CurveIt is the curve, which is bell shaped in structure. It is formed when the data having normal distribution is plotted.Normal DistributionIt is the distribution that describes a frequency distribution comprising of data points which resembles a bell shape structure. The normal distribution shows important properties that are necessary for performing various statistical tests for different types of applications.Null HypothesisIt is the hypothesis that states that there is no difference among and between the groups. It is in sharp contrast to alternative hypothesis that states that between two or more groups there is some differenceObserva tion UnitIt is the actual unit which is subjected to observation during the course of study.6.15 Case studyLet us assume that a manufacturer of the light bulbs wants to produce bulbs with a mean life of constant of gravitation hoursIf the lifetime is shorter, he/ she will lose customers to his / her competitors if the lifetime is longer, he / she will have a very high production cost because the filaments will be excessively thick.In order to see whether the production process is working properly a sample of the output is taken to test the hypothesisA two tailed test is used because he / she does not want to deviate significantly from 1000 hours in either direction. Therefore the null hypothesis is rejected.