00:00 0.17 KB/S 6 11 40 Quarter: 4 Week: 5 MELCs: 1. Computes for the test statistic value (population proportion) (M11/12SP-IVf-1); 2. Draws conclusion about the population proportion based on the test statistic value and the rejection region (M11/12SP-/Vf-2); and 3. Solves problems involving test of hypothesis on the population proportion (M11/12SP-IVf-g-1) Title of Textbook/LM to Study: Statistics and Probability > Chapter: 5 Pages: 271-280 Topic: Testing Hypothesis Involving Population Proportions > Objectives:1. Computes for the test-statistic value of the population proportion. 2. Draws conclusion about the population proportion based on the test statistic value and the rejection region. 3. Solves problems involving the test of hypothesis on the population proportion. Let Us Discover In this lesson, you are going to learn how to compute the test-statistic value of population proportion, draw conclusions about the population proportion based on the statistic value and the rejection region, and solve problems involving the test hypothesis on the population proportion. To calculate the appropriate test-statistic value for the population proportion the following formulas are needed: a. Sample proportion p = = where: p is the sample proportion (read as "p hat) x is the number of desired outcomes n is the sample size b. Value of z-test statistic for population proportion: z = - Po(1-PO) Where: z is the test statistic for the population proportion p is the sample proportion Po is the hypothesized population proportion n is the sample size It is necessary that in hypothesis testing, you give the correct conclusion and decision to avoid error. In drawing the conclusion, you may apply the critical value approach. In this approach, the computed test-statistic is compared with a critical value at a given significance level. Please refer to the following table. GSC-CID-LRMS-ESSLM, v.r. 02.00, Effective April 21, 2021 Type of Test for Statistical Hypothesis Directional/ One-tailed Test Non-directional/ Left-tailed test Right-tailed test Two-tailed test Rejection region Rejection region Rejection region Signifi- Confi- cance dence level (a) Level a 1 % or 0.01 99% or 0.99 Z=-2.326 Z = 2.326 Z = +2.567 5% or 0.05 95% or 0.95 Z = -1.645 Z = 1.645 Z = $1.960 10% or 0.10 90% or 0.90 Z = -1.282 z = 1.282 Z = #1.645 REJECT H, if Z S -z. REJECT H, Z Z Z. REJECT H, if Z s -z or > > Decision/Conclusion Fail to REJECT Ho, Zzz. Fail to REJECT H. if Z s z. if Z 2-Z. Fail to REJECT H. if -z s2 sz. If the computed z-value falls in the rejection region, REJECT the null hypothesis (Ho). The conclusion would be: Therefore, at level of significance, there is sufficient evidence that If the computed z-value does not fall in the rejection region, FAIL TO REJECT the null hypothesis (Ho). The conclusion would be: Therefore, at_ level of significance, there is insufficient evidence that Note: Z is the computed test-statistic and z is the critical value at a given significance level. The concepts mentioned above are needed to solve problems involving hypothesis testing. In solving problems for a test of hypothesis on the population proportion using the critical value approach, follow these five (5) steps: 1. State the null and alternative hypotheses. 2. Choose the level of significance and determine if the test is two-tailed or one-tailed. 3. Calculate the appropriate test statistic. 4. Determine the critical value at a given significance level, draw the normal curve, and00:00 11.0 KB/S 6 11 40 2. Choose the level of significance and determine if the test is two-tailed or one-tailed. 3. Calculate the appropriate test statistic. 4. Determine the critical value at a given significance level, draw the normal curve, and identify the critical region or rejection region. 5. State your decision to either REJECT or FAIL TO REJECT the null hypothesis (H.). Finally, draw your conclusion. Let Us Try Activity 1. Fill Me Up! Directions: Compute the test statistic. Fill in each blank with the appropriate wordumber/symbols to complete the statement. Given: 1. Ho: The proportion of learners who plays online games is at most 85%. (p s 0.85) Ha: The proportion of learners who plays online games is more than 85%. (p > 0.85) 2. Level of significance: a =0.05, x = 66, n=75, po = 0.85 GSC-CID-LRMS-ESSLM, v.r. 02.00, Effective April 21, 2021 Solution: 3. Computed test statistic Sample proportion: p = = = 20 = 0.88 0.88-0.85 Z = - P-Po 0.88-0.85 Po(1-PO) 0.85(1-0.85) 0.85(0.15) 75 75 ZE (1) 4. The normal curve with corresponding critical value and computed test statistic value(z-value) _(2) _ (3) 5. Decision: Since the computed test statistics z = (4) is less than the critical value z = _ (5), we Fail to Reject the null hypothesis Ho. Conclusion: Therefore, at _(6) level of significance, there is insufficient evidence to claim that the proportion of learners who plays online games is at most 85%. Let Us Do Activity 2. Supportive Parents! Problem: A sample of 300 parents of learners from Maliwanag High School were randomly selected and 240 of them said they are willing to assist the schooling of their children through Modular Distance Learning. Does this data provide sufficient evidence to claim that less than 75% of parents indicated willingness to assist their children in Modular Distance Learning? Use a = 0.05. Complete the following table: STEPS SOLUTION 1. State the null and alternative Ho: hypotheses Ha: 2. Choose the level of a = significance and determine if the Type of test: test is two-tailed or one-tailed. 3. Calculate the appropriate Given: X = _, n= - Po = test statistic. a. Sample proportion, p = = p = b. Compute the test-statistic, z = P-Po Po(1-Po) Z= E OActivity 2. Supportive Parents! Problem: A sample of 300 parents of learners from Maliwanag High School were randomly selected and 240 of them said they are willing to assist the schooling of their children through Modular Distance Learning. Does th'ni data provide sufcient evidence to claim that less than ?5% of parents indicated willingness to assist their children in Modular Distance Learning? Use a = 0.05. Complete the following table: STEPS SOLUTION 1. State the null and alternative H": hypotheses. Hg: 2. Choose the level of a = significance and determine if the Type of test: test is two-tailed or one-tailed. 3. Calculate the appropriate Given: x= . n = . pa = _ test statistic. a. Sample proportion, 13 = i = b. Compute the test-statistic. z = 9-31., Natln) n Z= GSC-CfD-LRMS-ESSLM. VJ. [2.00, Effective W21. 2621 STEPS SOLUTION 4. Determine the critical value at a given significance level, draw The critical vdue the normal curve and identify the \"= at O=_ IS critical region or reieclion region. \\' l 7- : 7 .. '_ 5. Decide whether to reject or Decision: Since the computed test statistic z = _. is fail to reiect the null hypothesis. than the critical value 2 = or it does Draw a conclusion. not fall in the rejection region, we the null hypothesis. Ganclusion: Therefore. at significant level. there is evidence that the proportion of parents who indicated willingness to assist their children in Modular Distance . Activity 3. Be Wise! Scenario: In a survey. 200 Senior High Students of Masagana High School were interviewed if they want to get COVlD-1Q vaccine or not. Among the 200 respondents. 45 students confirmed to take the vaccine as soon as it is available. Test the hypothesis that 20 at: of the Senior High School students wants to get vaccinated using a = 0.01 as the level of significance. (Please use separate sheet for your answer). Belecina. Rene R.. Baccay Elisa S.. and Mateo. Efren B. Statistics and Probability. Manila: Rex Bookstore, Inc., 2016 SSLM Development Team