MAT 152: Chapter 8:3 Name:_________________________________ PART I: Hypothesis Testing LAB Activity The Significance of a Coin I. Purpose: This activity is intended to illustrate properties of hypothesis testing and to describe how to perform hypothesis tests on a proportion. II. Materials and Introduction: 1. Each person should have 10 pennies and a 16-ounce plastic cup 2. Examine one of the pennies. There are two possible outcomes when a PENNY is tossed landing completely as TAIL or HEAD. 3. Estimate p, the proportion of the time that a PENNY will land on TAIL when tossed. 4. We will assume that p is approximately 50% and test the claim that the population proportion of Pennies that land completely on Tail is less than 50%. 5. We will assume also that p is approximately 35% and test the claim that the population proportion of Pennies that land completely on Tail is different than 35%. III. Experiment: The investigation is as follows: 6. Put 10 Pennies into the cup 7. Gently shake the cup twice to help mix up the coins. 8. Tip the cup so the bottom of the rim is approximately 1 - 2 inches from the table and spill the coins. 9. Count the number of pennies that land completely on Tail. 10. Return the coins to the cup and repeat until you have spilled the coins 5 times. 11. Record your results on the Data Table. Data Table: Toss Number Number of Pennies Landing Completely on Tail 1 2 3 4 5 Total IV. Questions 1 We treat the 50 results for each student as 50 independent trials. Actually, each student has ten independent trials of 5 tosses each. We make the assumption that the 10 tosses within a trial are roughly independent to expedite data collection. 1. We will assume that p is approximately 50% for the following two tests. a. Test the claim that the population proportion of Pennies that land completely on its Tail is different than 50% at = 10% level of significance. State hypotheses and : Calculate the evidence - State test used and numbers typed into the calculator. Clearly state the p-value. State the complete decision rule then state clearly your decision. State your conclusion in context to the problem. 2 b. Test the claim that the population proportion of Pennies that land completely on its Tail is less than 50% at = 10% level of significance. State hypotheses and : Calculate the evidence - State test used and numbers typed into the calculator. Clearly state the p-value. State the complete decision rule then state clearly your decision. State your conclusion in context to the problem. 2. We will assume that p is approximately 35% for the following two tests. a. Test the claim that the population proportion of Pennies that land completely on its Tail is different than 35% at = 5% level of significance. State hypotheses and : Calculate the evidence - State test used and numbers typed into the calculator. Clearly state the p-value. 3 State the complete decision rule then state clearly your decision. State your conclusion in context to the problem. b. Will your decision change if you test at = 10% level of significance? Explain why or why not. 3. Give an intuitive justification for why changing the sample size may result in changing the conclusion about a null hypothesis. PART II: Hypothesis Testing Practice Classwork 4 Identify the claim, null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that address the original claim. 4. A manufacturer considers his production process to be out of control when defects exceed 3%. In a random sample of 85 items, the defect rate is 5.9% but the manager claims that this is only a sample fluctuation and production is not really out of control. At the 0.01 level of significance, test the manager's claim. a) State the CLAIM: b) STEPS: 1) State claim into symbols: 2) Construct H0 and H1: 3) Identify significance Level: 4) Testing statistics: 5) P-value: 6) Conclusion: 5. A nationwide study of American homeowners revealed that 64% have one or more lawn mowers. A lawn equipment manufacturer, located in Omaha, feels the estimate is too low for households in Omaha. Can the value 0.64 be rejected if a survey of 490 homes in Omaha yields 331 with one or more lawn mowers? Use the 0.05 level of significance. a) State the CLAIM: 5 b) STEPS: 1) State claim into symbols: 2) Construct H0 and H1: 3) Identify significance Level: 4) Testing statistics: 5) P-value: 6) Conclusion: 6