15:07 10 . 8.00 KB/S Ill 59 Quarter: 4 Week: 3 MELCs: 1. Computes for the test-statistic value (population mean) (M11/12SP-IVd-1); 2. Draws conclusion about the population mean based on the test- statistic value and the rejection region (M11/12SP-IVd-2); and 3. Solves problems involving test of hypothesis on the population mean (M11/12SP-IVe-1). Title of Textbook/LM to Study: Statistics and Probability Chapter: 4 Pages: 193-201 Topic: Test of Hypothesis Using z-test Objectives: 1. To compute for the test-statistic value (population mean). 2. To draw conclusion about the population mean based on the test- statistic value and the rejection region. 3. To solve problems involving test of hypothesis on the population mean. Let Us Discover A test statistic is used in a hypothesis testing when you are deciding to support or reject the null hypothesis. In large sample test concerning the population mean, the test statistic to be used is the ze. The z-test statistic is used when the sample size is greater than 30 (n 230), or when the population is normally distributed and a is known. Formula: where: - H Zc = z - test statistic or z - computed x = sample mean Ho = population mean = population standard deviation n = sample size Steps in hypothesis testing using the z-test statistic 1. State the hypotheses 2. Identify the level of significance and determine if the test is two-tailed or one-tailed. 3. Compute the test statistic 4. Determine the critical value, draw the normal curve, and identify the critical region 5 . State your decision and make a final conclusion Example 1. A light bulb manufacturer claims that the average lifetime of a bulb is 30 months. The standard deviation is 7 months. Forty bulbs are selected and the average lifetime is found to be 26 months. Should the manufacturer's statement be rejected at a = 0.05? GSC-CID-LRMS-ESSLM, v.r. 02.00, Effective April 21, 2021 Solution: Step 1. Ho: u = 30 months Step 4. Since a = 0.05 and it is two-tailed, Ha: H # 30 months the critical values are Za/2 = $1.960 Step 2. a = 0.05; = 0.025; two-tailed test > > Step 3. Test - statistic Given: x = 26 , u = 30 , 0 = 7 , n = 40 X-M _ 26-30 -4 -4 = = -3.61 -3.61 -1.960 1.960 V40 1.107 6.325 Step 5. Decision/Conclusion: Since Zc =-3.61 48 the critical value is Za = 1.282 E15:07 19 . 0.08 KB/S 59 Solution: Step 1. Ho: H S 48 Step 4. Since a = 0.10 and it is one-tailed, Ha: H > 48 the critical value is Za = 1.282 Step 2. a = 0.10; one-tailed test Step 3. Test - statistic Given: x = 50.5, u = 48 , 6 = 3.8 , n = 35 Z = 50.5-48 2.5 2.5 1.282 3.91 3.8 38 0.64 = 3.91 735 5.916 Step 5. Decision/Conclusion: Since Zc =3.91 > Z a =1.282, thus, we reject the Ho. Therefore, there is enough evidence to support the claim that a can of juice contains a mean carbo content of over 48g. Let Us Try Activity 1: "YOU COMPLETE ME!" Direction: Complete the solution in each of the following problems. Problem 1: A barangay official initiates a cycling competition for an expert group of men cyclists. He claims that the average speed of a finisher is greater than 23.5 kph. He took a random sample of 36 cyclists with an average speed of 25.4 kph and a standard deviation of 3.7 kph. Is there enough evidence to support the barangay official's claim? Use a = 0.01 GSC-CID-LRMS-ESSLM, v.r. 02.00, Effective April 21, 2021 Solution: Step 1. Ho: Step 4. Since a = and it is Ha: the critical values are Za = Step 2. a = test Step 3. Test - statistic Given: x = ,0= -,n=_ Z= Step 5. Decision/Conclusion: Let Us Do Activity 2: "YOU COMPLETE ME! V2" Problem 2: The manufacturer of a battery claims that the mean life of it is 8 months. An agency took a sample of 40 such batteries with a mean life of 7 months and a standard deviation of 2.25 month. Using 10% significance level, is there sufficient evidence to reject the claim? Solution: Step 1. Ho: Step 4. Since a = and it is Ha: the critical values are Za/2 = Step 2. a = test Step 3. Test - statistic OLet Us Do Activity 2: \"YOU COMPLETE ME! V2" Problem 2: The manulacturerof a hatter}.r claims that the mean life of it is 8 months. An agency\"r took a sample of 40 such batteries with a mean life of 7 months and a standard deviation of 2.25 month. Using 10% significance level, is there sufficient evidence to reject the claim? Sulution: Step 1. Ha: Ha: Slap2.cr= Step 4. Since a = and it is , the critical values are Z\" 1,2 = Step 3. Test statistic Given: ?= \"u z=,r=- =_ 35 3' _ Step 5. DecisionII'Conclusion: II a I GSGCl'D-LRMS-ESSLM, VJ. [112.00, Effective April2'l. 2821 Acvilf 3: \"LET'S FIND IT!\" A researcher claims that the average load consumption of Grade 11 students for their online class is 93,000 per month. In a sample oi 36 students, the average monthly load consumption was 92,750 with the standard deviation of '550. Is there enough evidence to support the claim at a = 0.05? Rubric lor Problem Solving 4 3 2 1 Followr the steps Follow the steps Follow the steps Attempt to solve to come up with to come up with but come upwith but does not a correct a solution but a an entirely follow the steps solution and part of the wrong solution that led to a draw at the solution led to and led to wrong solution correct incorrect incorrect and incorrect conclusion conclusion conclusion conclusion