Alternative hypothesis Essay

A venture is a statement active the value of a universe parameter. The nation of interest is so magnanimous that for various reasons it would not be feasible to study all the items, or persons, in the population. Analternative to measuring or interviewing the entire population is to take a en hear from the population of interest. We can, therefore, test a statement to determine whether the empirical rise does or does not support the statement. Hypothesis testing starts with a statement, or assumption, about a population parameter such as the population mean. As noted, this statement is referred to as a scheme.A hypothesis might be that the mean monthly commission of salespeople in retail data processor stores is $2,000. We cannot contact all these salespeople to ascertain that the mean is in fact $2,000. The cost of locating and interviewing every calculating machine salesperson in the whole country would be exorbitant. To test the validity of the assumption (population me an = $2,000), we must select a sample from the population consisting of all computer salespeople, calculate sample statistics, and based on certain stopping focus rules hold or reject the hypothesis.A sample mean of $1,000 for the computer salespeople would sure cause rejection of the hypothesis. However, suppose the sample mean is $1,995. Is that close enough to $2,000 for us to go for the assumption that the population mean is $2,000? Can we attribute the difference of $5 between the two means to sampling (chance), or is that difference statistically significant? Hypothesis testing is a procedure based on sample evidence and luck theory to determine whether the hypothesis is a reasonable statement and should not be rejected, or is unreasonable and should be rejected.The trifling hypothesis and the alternative hypothesisThe nugatory hypothesis is a tentative assumption do about the value of a population parameter. The alternative hypothesis is a statement that will be cur rent if our sample data take into account us with ample evidence that the void hypothesis is false.Five-step procedure for testing a hypothesisThere is a five-step procedure that systematizes hypothesis testing. Thesteps are Step 1. State zero and alternative hypotheses.Step 2. Select a take of substance.Step 3. Identify the test statistic.Step 4. Formulate a decision rule.Step 5. Take a sample, arrive at decision (accept H 0 or reject H 0 and accept H 1 ).The first step is to state the hypothesis to be tested. It is called the null hypothesis, designated H 0 , and read H sub-zero. The capital letter H stands for hypothesis, and the subscript zero implies no difference. The null hypothesis is set up for the purpose of either accepting or rejecting it. To put it another way, the null hypothesis is a statement that will be accepted if our sample data fail to provide us with convincing evidence that it is false.It should be emphasized at this point that if the null hypothesis is accepted based on sample data, in effect we are saying that the evidence does not consent to us to reject it. We cannot state, however, that the null hypothesis is true. That means, accepting the null hypothesis does not prove that H 0 is true to prove without any doubt that the null hypothesis is true, the population parameter would overhear to be known. To actually determine it, we would have to test, survey, or count every item in the population and this is usually not feasible.It should also be noted that we frequently begin the null hypothesis by stating there is no significant difference between. When we select a sample from a population, the sample statistic is usually different from the hypothesized population parameter. We must make a judgment about the difference is it a significant difference, or is the difference between the sample statistic and the hypothesized population parameter due to chance (sampling)?To resolve this question, we conduct a test of significance . The alternative hypothesis describes what you will believe if you reject the null hypothesis. It is often called the research hypothesis, designated H 1 , and read H sub-one, so the alternative hypothesis will be accepted if the sample data provide us with evidence that the null hypothesis is false. The take aim of significanceThe next step, after setting up the null hypothesis and alternative hypothesis, is to state the level of significance. It is the guess we assume of rejecting the null hypothesis when it is actually true. The level of significance is designated , the Greek letter alpha.There is no one level of significance that is employ to all studies involving sampling. A decision must be made to use the 0.05 level (often stated as the 5 percent level), the 0.01 level, the 0.10 level, or any other level between 0 and 1. Traditionally, the 0.05 level is selected for customer research projects, 0.01 for quality assurance, and 0.10 for political polling and the chosen le vel is the probability of rejecting the null hypothesis when it is actually true.The test statisticThe test statistic is a value, determined from sample information, used to accept or reject the null hypothesis. There are many test statistics z , t , and others. The decision rule acceptance and rejection spheresA decision rule is simply a statement of the conditions under which the null hypothesis is accepted or rejected. To accomplish this, the sampling distribution is divided into two regions, aptly called the region of acceptance and the region of rejection. The region or field of force of rejection defines the location of all those values that are so large or so small that the probability of their occurrence under a true null hypothesis is rather remote.Chart 4.1 portrays the regions of acceptance and rejection for a test of significance (a one-tailed test is being applied and the 0.05 level of significance was chosen). Note in Chart 4.1 The value 1.645 separates the regions o f acceptance and rejection (the value 1.645 is called the critical value). The area of acceptance includes the area to the left of 1.645. The area of rejection is to the right of 1.645.Thus, the critical value is a number that is the dividing point between the region of acceptance and the region of rejection.Chart 4.1. Sampling distribution for the statistic z regions of acceptance and rejection for a right-tailed test 0.05 level of significance