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It is believed that the average daily allowance of grade 1 1 students in private school is P100 pesos. To verify this claim, a high school principal has conducted a study by randomly choosing 150 grade 11 students in his school. It has been found out that the average daily allowance of these students is P105 with a standard deviation of P2.50. Based on these sample data, it can be concluded that the claim is true. This problem is an example of situations that are frequently encountered in testing the hypothesis. In this lesson, we shall learn the basic concepts that are necessary in conducting the test of hypothesis. 1.12. Preparatory Activity: Match each symbol in Column B with the correct term in Column A. COLUMN A COLUMN B 1. Population mean a. x 2. Sample standard deviation tnobut? to amen b. S 29290loqud to 212 3. Population standard deviation C. N 4. Sample size d. H or gnlovni as 5. Population size e. n Stif-lest ni 29on 6. Sample mean f. o .zonilgiozib insistlib mi amoldong Lesson: 2010YlullI In many cases, we formulate hypotheses or tentative statements to explain facts about a phenomenon or situation based on available evidences. Suppose that there is a claim that the average monthly income of Filipino families who belong to the low income bracket is P8000 or less than P8000, or greater than P8000. To find out whether our hypothesis is TRUE or FALSE, we can select a random sample data, we can determine the average income of Filipino families. In other words, we can make a generalization about the population, using a sample. This process is called HYPOTHESIS TESTING. s or sisluto' A statistical hypothesis is a statement about the numerical value of a population parameter. It is a statement or tentative assertion which aims to explain facts about a certain phenomenon, A hypothesis needs to be resolved whether it is true or false. Thus, it must be subjected to statistical testing procedure known as TEST OF HYPOTHESIS or HYPOTHESIS TESTING. If the hypothesis is found to be TRUE, it is accepted, if it is found to be false. it is rejected. 970 Two kinds of hypothesis: 1. NULL HYPOTHESIS- denoted by Ho; is a statement that there is no difference between a parameter and a specific value. zsvilogido offjoon2 \\ersginT animing.! 2. ALTERNATIVE HYPOTHESIS- denoted by Ha; is the opposite or negation of the null hypothesis. It is a statement that there exist a difference between a parameter and specific value. 2Sbi 9) usla siclummol bris smits V Note: when we formulate the null or alternative hypothesis, we examine the claim or the conjecture regarding the population parameter. B no ageofoqrd swimsits bus fun stonqoiqqs ord siloamnot near nouslugog Question: How do we formulate the null hypothesis and alternative hypothesis for a given conjecture or claim? Isnoitoorib Example: bolist mein no bolist fol zi fest Innoitostib s werbordw onismoss CLAIM: The average monthly income of Filipino families who belong to low income bracket is P8000 Ho : The average monthly income of Filipino families who belong to low income bracket is P8000 (H = 8000) Ha : The average monthly income of Filipino families who belong to low income bracket is NOT P8000 ( u # 8000 ) * **Notice that the null hypothesis is expressed through the use of the "equal" symbol while the alternative hypothesis ix expressed by "not total" symbol because the claim conjecture does not specify any direction.TYPE OF TEST !:A statistical test may either be directional (one-tailed) or non-directional (two-tailed). We can determine art;whether a test is directional or non-directional by looking at how the alternative hypothesis is expressed. [ffii DIRECTIONAL TEST o A test of any statistical hypothesis where the alternative hypothesis is expressed, using less than () is called directional test since the critical or rejection region lies entirely in one tail of the sampling distribution. NONDIRECTIONAL TEST worl is you O A test of any statistical hypothesis where the alternative hypothesis is written with not equal (#) is test off tol called a nondirectional test or two-tailed test since there is no assertion made on the direction of the difference. The rejection region is split into two equal parts, one in each tail of the sampling distribution. 10 / in .aizordoqvil Ilun ords boston to bepoos of isthorn noiziosb s odel + Non-Directional & Directional Hypotheses . Nondirectional offof Sieshoqvid llun sili ganboston 10 griqgoos no sbiosb ow ob wolf H : there is no effect: ( X = H) ofasi fsoilaisle sishqones ofdye splay Inside oth sommers I H,: there IS an effect: onlev Isonyo ord bas koigon nobiosis ed ward S ziesritoquid Ilun sit 10919 ( X # p) 09jor or ni allot suk betugmoo APPLY 2-TAILED TEST ingoos saidnorito 2.5% chance of error in -1.96 1.96 : I olqmaza each tail . Directional ni east ai ainobute sgelloo to sonswolls videow sgrieve ofT :mind? H, : sample mean is larger ai aimebute ogolloo Moontolls vidsow ognievs onT :OH than population mean "X>u) . Ooci 1 math 22of zi aimsbuse agslide to sonswoks window ogslovs onT :BHI mads east sthi seurosd fothe *$ Hol s ai aith vileoiliosqa A toot helict Jonoilogrib zi airIT esil noigen nobiosis simo APPLY 1-TAILED TEST fordrogvi ovitsmails ord gait.65qus ni beau asw lodmg? . 5% chance of error in .nobudinzib gailqrise Sdi to list fiel odr ni vlonine one tail :5 siqmsx] TYPES OF ERROR 0021 'I nerds Totheng ai atmsbute sgolloo to sonswolls videow ogsievs oriT :mist In decision making, we sometimes make a wrong decision. Likewise, when we test a hypothesis, there is a possibility that we shall also commit an error of accepting or rejecting the hypothesis. There are two types of errors: TYPE I error and the TYPE II error up sioM best bolistogo to last longtosub s gels at zidT TYPE I error- occurs when we reject the null hypothesis when it is true, it is also called alpha error noigs (a error) maderib unique and to list idgnods sey TYPE II error- occurs when we accept the null hypothesis when it is false. It is also called the beta error (B error) I YIMITA zieshoqed sviennois ne 10 eiestdogvid lion s ai aniwollol oh wordisw vingbl .A LEVEL OF SIGNIFICANCE blo aisy FI ai amsbule asvols sbrig to sys 5grows ondT The probability of committing Type I error is called the level of significance. It is denoted by the Greek lettera. Thus the value of a tells us the probability of making an error in rejecting the null hypothesis when it is actually true. The choice for the value of the significance level is determined by the researcher. This depends on the risk or degree of confidence the researcher is willing to take in committing Type I error. The commonly used levels of significance are 0.05 and 0.01. The level of significance should be set before testing the hypothesis. estunim Of ai foorloe of amori moil plummos of ome 9gases andExample: A 0.01 level of significance means the researcher is willing to take 1% error in making a decision. It also implies that he is 99% confident that he will make the right decision. Likewise a 0.05 level of confidence means that the researcher is willing to take 5% error in making a decision. It also implies that he is 95% confident that he will make a right decision. O STEPS IN TESTING THE HYPOTHESIS Whenever we test hypotheses, we follow these steps. noidnaib gudque onit to him 1. Identify the claim and formulate the null (Ho) and the alternative (H.) hypothesis,, 19 / 2. Set the level of significance and determine whether the test is one-tailed or two-tailed by looking at how the alternative is expressed. Decide on the test statistic to be used and find the critical value for the test. Draw or illustrate the rejection region. nowudhlab 3. Compute the test value, using the test statistic or formula for the test. 4. Make a decision whether to accept or reject the null hypothesis. 5. Formulate a conclusion by answering the research question, ACCEPTING OR REJECTING THE NULL HYPOTHESIS Isnoiton i0-nol How do we decide on accepting or rejecting the null hypothesis? Follow these steps. nov . 1. Determine the critical value, use the appropriate statistical tables. ( ) on al exaril H 2. Draw the rejection region and the critical value. 3. If the test value or the computed value falls in the rejection region, then reject the null hypothesis; otherwise accept the null hypothesis. T23T Q3JIAT-S YJ99A Example 1: ae rher wa nons to consrio de.s list dose Claim: The average weekly allowance of college students is less than P 1500. Ho: The average weekly allowance of college students is P 1500. room glumsa , H ugog nerit Ha: The average weekly allowance of college students is less than P 1500. (