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WCU ECO 252 - ECO 252 Graded Assignment 3

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252grass3-051 3/24/05 (Open this document in 'Page Layout' view!)Name: Class days and time:Please include this on what you hand in!Graded Assignment 3In your outline there are 6 methods to compare means or medians, methods D1, D2, D3, D4, D5a and D5b. Method D6 compares proportions and method D7 compares variances or standard deviations. In all the following cases, identify 0H and 1H and identify which method to use. If the hypotheses involve amean, state the hypotheses in terms of both  and 21D. If the hypotheses involve a proportion,state them in terms of both p and 21ppp . If the hypotheses involve standard deviations or variances, state them in terms of both 2 and 2221 or 2122. All the questions involve means, medians, proportions or variances. (Most problems are highly edited versions of problems in McClave, et. al.)Note: Look at 252thngs (252thngs) in the syllabus supplement before you start (and before you take exams).1. We have the amount spent by a sample of 25 pharmaceutical firms on research in 2002 and again for the same firms in 2004. We assume that the underlying distributions are Normal. Was the average amount spent in 2004 above the average amount spent in 2002? 2. Assume that you had the same data and a similar task to Problem 2 but your preliminary analysis indicated that the underlying distributions were highly skewed to the right.3. You have the grades of a sample of 15 traditional university students and 2 grades of a sample of 13 non-traditional university students, do these differ on average? Assume that preliminary analysis indicates that the variances of grades of the two groups are similar and presume an underlying Normal distribution.4. Since the results of Problem 3 were inconclusive, you take new samples of 250 traditional university students and 150 non-traditional students, again you assume that the underlying distribution is Normal, but you do not bother to compare variances. You are still trying to find out if grades of the two groups differ.5. A recheck of the data in Problem 4 indicates that the underlying distribution is far from Normal, but you are still trying to find out if the grades of the two groups differ. 6. If 10 out of a group of 80 randomly chosen people who have received information on your product are inclined to buy it and 12 out of a group of 81 randomly chosen people are inclined to buy your product after receiving the same information and seeing your commercial, does the commercial increase the proportion who will buy your product?7. Have new procedures decreased the variability of delivery times? Two samples have been taken and youknow 1xand 1s taken before the new procedures were instituted, and 2x and 2s, taken afterwards. There seems to be little difference between average delivery times before and after.8. A paper company wishes to know whether a new procedure has decreased the amount of time it takes to unload trucks. What are the hypotheses this implies? Two samples are taken with the results below. How do we decide whether to use Method D2 or D3? What hypotheses, etc do we test to make this decision?Old Method New Method501n 502n4.251xminutes 3.272xminutes1.31sminutes 7.32sminutes9. You have the following data and want to see if means are similar before and after. Assume that the parent distributions are Normal.Person Before After 1 82 92 2 60 72 3 55 57 4 97 104 5 79 8910. An experiment at Duke University was conducted to see if ability to identify food by taste and smell decreases by age. One food (mushed apple) was correctly identified by 81out of 100 students and by 51 outof 100 older people. Extra Credit: In Method D6, we assume that we are comparing proportions from two independent samples. In the McNemar Test we compare two proportions taken from the same sample. Assume that twodifferent questions are asked of the same group with the following responses.2221121121xxxxnoyesnoyesquestionquestion So, for example 21x is the number of people who answered no to question 1 and yes to question 1. nxxxx 22211211, nxxp12111 and nxxp21112. If we wish to test 211210:H:Hpppp, let 21122112xxxxz but the test is valid only if 102112 xx A famous example of this concerns a debate between candidates, question 1 is whether the respondent supports candidate 1 before the debate and question 2 is whether the respondent supports candidate 1 afterthe debate. The data is 281372721noyesnoyesquestionquestion and the question is whether the debate has changed the fraction supporting candidate 1. Write this out as a hypothesis test and do the test.Note: This is a version of the Chi-Square Test – Recall that  EEO22. If we take 11x and22x as given, and assume that the null hypothesis is correct, then the table already given,2221121121xxxxnoyesnoyesquestionquestion is our O, and the numbers in the 12x and the 21x slots must be equal 2for there to be no change in preferences, so that out E is 2221122112112221xxxxxxnoyesnoyesquestionquestion. This means that two of the four terms in  EEO22 are zero and the remaining terms are222221122211221211222112122xxxxxxxxxx  211222112xxxx. But 2 has only one degree of freedom, and, since 2 is defined as a sum of 2z, we can take a square root and say 21122112xxxxz .


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