Activity 3 Developing Intuition about Significance Fair Coins If we.pdf

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Activity 3: Developing Intuition about Significance: Fair Coins If we are flipping a coin, how large a proportion of heads do we need to get in order to claim evidence that the coin is biased to give more heads than tails? If the coin is fair, the proportion of heads should be 0.5 , so our null and alternative hypotheses are H0:p=0.5 vs Ha: p>0.5, where p is the proportion of heads. First For each situation below, make a guess about whether or not you think that sample outcome would give convincing evidence for a biased coin (Yes or No) Second Now using Statkey (using at least 5,000 simulated samples) find the p-value in each case above and indicate whether (at a 5% level) there is convincing evidence that the coin is biased. If you are working in a group, consider divide and conquer, before discussing results. Examine the results from the p-values. Consider each of the factors below. Decide whether or not each has an impact on whether or not a sample proportion shows significance. 1. The sample size 2. The sample proportion 3. The number of simulated samples in the randomization distribution.

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Hypothesis Testing Hypothesis The formal testing of hypothesis is a critical step not to be ignored. One of the jobs of statistics is to reduce the uncertainty in our decision making. It does so by helping to identify assumptions and check the validity, in essence, what is really there. It is my personal preference to evaluate stocks or mutual funds to see if they actually exceed the average market return of 10%. The 10% return is the historical return on stocks over the past 75 years, however, each year has its own unique return. When doing so, I am interested in did this mutual fund exceed the 10% annual return. When you look at hypothesis testing there are three ways you can set them up. There are as follows: HO: = H1: not equal Word In story problem: Is Different Ho: < or = H1: is greater than Word In story problem: more than, increased HO: > or = H1: Is less than Word In story problem: decreased, dropped The hypothesis come in “pre-packaged sets” so you can’t mix and match. So when you are setting them up, look at the alternative (H1) in setting them up. Many times this is the decision that interests you the most. In this case, I wanted returns that exceeded ten percent, so I looked at the alternative hypothesis of greater than when setting up the process. What is helpful in thinking about the hypothesis and alternative hypothesis are the unique qualities of the null or HO, hypotheses. The HO hypothesis has unique characteristics. The unique characteristics is that you assume there to either be “no difference” or status quo. So, I set the hypothesis up as follows: HO: return is less than or equal to ten percent H1: return is greater than ten percent For the hypothesis test, I could have chosen to have it set up two other ways and those are: HO: the return is equal to ten percent H1; the return is not equal to ten percent HO: The return is greater than or equal to ten percent H1: The return is less than ten percent. What is helpful in thinking about the hypothesis and alternative hypothesis are the unique qualities of the null or HO, hypotheses. The HO hypothesis has unique characteristics. The unique characteristics are that you assume there to either “no difference” or status quo. In the stating of HO there is always an implied equal. To help you understand this concept lets take a trip to the local vending machine. Hypothesis Test Thinking and a Vending Machine Imagine yourself walking up to a vending machine. You want to purchase a bottle of Pepsi for a $1.00. You walk up to the vending machine and assume you are going to put your dollar in the machine, press the Pepsi button, and the machine will dispense the bottle of Pepsi. Do you walk up to the machine, knowing that it is not going to give you your bottle of Pepsi after you insert your dollar? If so, would you proceed with the transaction. No you wouldn’t make the transaction and willingly lose your doll.

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