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a Let Us Study A statistical hypothesis is a statement about a parameter and deals with evaluating the value of parameter. In statistical hypothesis testing, there are always two hypotheses: the null and alternative hypotheses. Below is a comparison between the two. Null Hypothesis (Ha) Alternative Hypothesis [Ha] It states that there is no difference between population parameters (such as mean, standard deviation, and so 0113 and the hypothesized value. There is no observed effect. The null hypothesis is often an initial claim that is based on previous analyses or specialized knowledge. It states that the population parameter has some statistical signicance (smaller, greater, or different than) with the hypothesized value. There is an observed effect. The alternative hypothesis is what you might beheve to be true or hope to prove true. To state the null and alternative hypotheses correctly: 1. Identify the parameter in a given problem. 2. Identify the claim to be tested that may show up in null or alternative hypothesis. 3. Translate the claim into mathematical symbols / notations. 4. Formulate rst the null hypothesis (Ho) then alternative hypothesis (Ha) based on the three different ways in writing hypothesis as illustrated below: Ho:p=k Ho:|.lk Haiuljk HrH-ik Ha:p.>k Ha:u is increased ?IS,OOO and greater than falls at alternative hypothesis, Ha: u > s15, 000. Since you have already formulated the alternative, the null hypothesis will be Ho: [1 s ?15, 000 as complement of >. You can also write your null hypothesis as Ho: 11 = ?15, 000. Ho: [1 s ?15, 000 or Ho: [1 = ?15, 000 Ha: [1 > ?15, 000 (claim) 3. Holistic Fitness Center claims that their members reduced an average of 13 pounds after joining the center. An independent agency wanted to check this claim took sample of 40 members and found that they reduced an average of 12 pounds with the standard deviation of 4 pounds. Determine the null and alternative hypothesis. Solution: In this example, the parameter to be tested is the average and the claim is reduced of 13 pounds. The claim that pertains to the parameter has the notation of () as the complement of (5). Therefore, alternative hypothesis is Ha: It > 240. Ha: I1 s 240 or Ho: I1 = 240 (claim) H\": p. > 240 One-Tailed and Two-Tailed Test The alternative hypothesis can take another form depending on the value of the parameter. The parameter may increase, decrease, or changed from the null value. An alternative hypothesis predicts not only the difference of sample mean from the population mean but also how it would be different in a specic direction lower or higher. This test is called a directional or onetailed test because the rejection region is entirely within one tail of the distribution. On the other hand, some hypotheses predict only that one value will be different from another, without additionally predicting which will be higher. The test of such a hypothesis is nondirectional or two tailed because an extreme test statistic in either tail of the distribution (positive or negative) will lead to the rejection of the null hypothesis of no difference. One-Tailed Two-Tailed 0 Alternative hypothesis contains the 0 Alternative contains the greater than (>) or less than [ 7h: I71 120, 000. This hypothesis uses inequality symbol (>) so it is onetailed test and it uses greater than which specically called for the righttailed test. Ho : u = 120, 000 and Ha : u > 120, 000 (righttailed test) 3. The average waiting time of all costumers in a restaurant before being served is less than 20 minutes. Determine the hypotheses and the directional test. Solution: You may notice that the hypothesis used the phrase 'less than' which denotes that the alternative hypothesis is Ha : u