PERFORMANCE TASK (15 points) Write the null and alternative hypotheses in words and in symbols for each situation. Also, determine the type of test to be used: right-tailed, left-tailed, or two-tailed. Null Hypothesis Alternative Type of Test Hypothesis (2 points) (2 points) (1 point) Example: Jose claims that the The average length The average length average length of a pop of a pop song is 4 of a pop song is not song is 4 mins. He obtained mins. 4 mins. Two-tailed a sample of 10 pop songs to see if his claim is true Ho: H = 4 H1: H # 4 1. The net weight of a bag of chips is 45g. The quality assurance officer obtained a sample of 75 bags to determine if they have the correct weight. 2. A study says that the average height of senior high school student is 155 cm. To verify this, a grade 11 researcher obtained the heights of 100 students. An officer is concerned about the increasing number of feral animals. The officer wants to see if the average number of pets per household is less than 5.PERFORMANCE TASK (20 points) Perform the six steps in hypothesis testing on the following problems. Write the COMPLETE steps on your paper. In the past, the average number of children of a Filipino family is 6 with a population standard deviation of 2 children. A random sample of 55 families were selected and found to have an average of 3 children. Can we say that the number of children of a Filipino family has gone lower? Use a = 0.05. Step 1: Ho: The average number of (1-2) Hi: the average number of (3-4) Symbol: Ho : (5) H1: (6) Step 2: Type of Test: (7) Zerl : (8) a = (9) Step 3: Computed Value (t) Z = (10-12) Step 4: Decision Rule: Reject Ho if (13-14). Otherwise, DO NOT reject Ho. Step 5: Decision Since (15-16), then (17-18) the Ho. Step 6: Conclusion Thus, the claim is (19). The average number of (20).WRITTEN WORK (20 points) Choose the letter of your answer. 1) True or False: Significant level a represents the area of the rejection region. A. True B. False 2) Which is the correct symbol for the alternative hypothesis? A. Ho C. H B. H1 D. P 3) It is a statement which states that the parameter is not equal to its hypothesized value. A. null hypothesis C. conjecture B. alternative hypothesis D. hypothesis 4) Which is the correct symbol for the null hypothesis? A. Ho C. H B. H1 D. H 5) The manager of fast-food chain thinks that the mean weight of fries being served to customers is more than 100 grams which is the standard amount as stated in the food manual. What is the null hypothesis? A. Hi: p s 100 C. H1: [ > 100 B. H: U = 100 D. H4: H # 100 6) It is a technique used to evaluate claims about a population based on the characteristics of a sample. A. parametric testing C. correlation analysis B. hypothesis testing D. hypothesis analysis 7) Which of the following statements is NOT true for hypothesis testing? A. The null hypothesis must contain the equal symbol. B. Type II error is the probability of accepting a false null hypothesis. C. Type I error is the probability of rejecting a true null hypothesis. D. The symbol for confidence level is a. 8) A manufacturer claims that the mean lifetime of their lightbulbs is at least 368 hours. A sample of 53 lightbulbs were obtained to see if this is true. What are the null and the alternative hypotheses? A. Ho: P 368 B. Ho: [ 2 368, H1: p 273, H1: p 4.8, H1: p # 4.8 C. Ho: [ # 4.8, H1: U = 4.8 B. Ho: [ 93 C. Ho: [ = 93, H1: p # 93 B. Ho: U S 93, H1: p 93Name: Date: Grade and Section: Parent's Signature: Read your Statistics and Probability SIPack and answer the written work and performance task below. Your scores in this activity sheet will be recorded and graded. You may write your solutions and answers on this paper. Use additional sheets of paper if needed. WRITTEN WORKS (40 points) Part A Write TRUE if the statement is correct, otherwise write FALSE. (2 point each) 1. A one-sample hypothesis test can involve two or more samples. 2. A two-tailed test with a = 0.01 has z-critical values of 12.58. 3. A right-tailed test with a = 0.01 has z-critical value of 1.96. 4. A left-tailed test with a = 0.05 has z-critical value of -2.33. 5. Z-test is used when the population o is unknown. 6. Ho is rejected when the test statistic is in the critical region. 7. If u= 22, 0 = 8, n = 40 and x = 19, the test statistic is z = -2.37. 8. The significance level is equal to the area of the acceptance region. 9. If z =-1.43, 99% confidence, two-tailed test, then the z value is rejected. 10. If p= 55, o = 10, n = 48 and x = 40, the test statistic is z = -2.12. Part B A random sample of 25 cans of sardines showed an average of 172.4 grams with a standard deviation of 16.7 grams. Is the manufacturer's claim of an average weight of sardines of 175 grams true using a = 0.05 level of significance? 11. The null hypothesis is u =175. 12. The alternative hypothesis is u # 175. 13. The population standard deviation is 16.7. 14. The sample mean is 17.4. 15. The critical value is the boundary between the rejection region and non-rejection region. 16. Used t-test, two-tailed 17. The computed value is -0.75. 18. The critical values to be used is +2.064. 19. The decision is REJECT the Ho. 20. The average content of a can of sardines is 175 grams