Data Table: Toss Number 1 Number of Pennies Landing Completely on Tail 3 2 6 3 4 4 2 5 3 Total 18 I. Questions 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. 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. 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