HINTS AND TIPS SMALL PROJECT Comparing Proportions In this project you test the proportion of people who agreed (or disagreed) with a statement you made. You took the statements from a poll someone else conducted and the results of which were published on line. You were supposed to keep a copy of the original poll and the results. Chapter 10, p. 454 explains that you can do a two sided test of a hypothesis bout your proportion and that from the original poll. However, you must check to be sure that you can assume that the sampling distribution of the proportion is approximately normally distributed To do this perform this calculation where p is your proportion (phat = x/n) and n is the number in your random sample: Is np(1-p) greater than or equal to 10? If yes, continue as follows. Example 5 walks you through a hypothesis test. This contains formulas for mean of phat and standard deviation of phat where the mean is mean phat =p 1/2 standard deviation of phat = [p(1-p)/n] You test your observed proportion (phat) against the proportion in the original poll like this: z = (phat - original p)/ standard deviation of phat Now compare the z with the values in the table for the standard normal distribution. Is the z unusual? Is it significant at the alpha = .10 or alpha = .05 level? What if np(1-p) is NOT greater than or equal to 10? Let's say your null hypothesis is P=0.30 and Q=0.70 and the alternative P> 0.30 and Q < 0.70. The statistical test with be the binomial and the sampling distribution is given by the binomial expansion. The critical region consists of all valeus of x which are so large that the probability of their occurring under the null hypothesis is less than or equal to 0.05. Since the alternative hypothesis is directional, this is a one tailed region. In my hypothetical example, 30% of the population "agrees" or of 30 people questioned we HYPOTHESIZE that 30% replied agree and 70% replied disagree. We test this by calculating the probability that 30, 29, 29.... of the 30 in the sample "agreed". 30 30-30 30 P(30) = (0.3) (0.7) * 30!/ (30!)(30-30)! which ends up being (0.3) gives you the probability that all 30 had said yes. You can now calculate the probability of 29 agreeing by making 29 29-29 some substitutions. P(29) = (0.3) (0.7) * 29!/ (29!)(29-29)! gives you the probability that 29 had said yes. You can continue in this fashion and add up the probabilities to get the probability that some number of the 30 in the sample said yes. If the probability is less than or equal to 0.05 say, then you reject the null hypothesis. The textbook talks about small sample proportions. Some relevant links: calculate with this one: https://www.medcalc.org/calc/test_one_proportion.php others which explain what is going on are these: http://vassarstats.net/binomialX.html or http://stattrek.com/online-calculator/binomial.aspx Confidence Intervals see pages 345-347 and 350-351 for the book's views on interpretation. Page 449 explains a CI for the difference between two proportions. Small Project 2 Due December 16 by email The questions you used to conduct your poll were supposed to have come from a poll someone or some group used. In this project you test your results against those found in the original poll and calculate a confidence interval for your proportions. To test your proportion against that in the original poll, use the material in Chapter 10.1. Test using alpha =0.05 Your book explains the test of whether or not two proportions are the same as the difference between two proportions. You can let your proportion be phat 1 if you want. You should test the following hypothesis: H0: p your poll = p published poll HA: p your poll is NOT equal to p published poll. Calculate your test statistic. Determine whether to accept or reject the null hypothesis. Calculate a confidence interval for your proportion at alpha = 0.05. IF YOU DO NOT HAVE THE ORIGINAL PROPORTION FROM THE POLL for some reason, you can still do this. Your hypothesis then becomes H0: p my poll = 0 HA: p my poll is NOT equal to 0 SEE OTHER MATERIALS on Blackboard for some additional help.
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