252grass3 061 10 27 06 Open this document in Page Layout view Name Class days and time Please include this on what you hand in Graded Assignment 3 In your outline there are 6 methods to compare means or medians methods D1 D2 D3 D4 D5a and D5b Methods D6a and D6b compare proportions and method D7 compares variances or standard deviations In the following cases identify H 0 and H 1 and identify which method to use Method E1 is a chi squared test that compares multiple proportions Method F1 is analysis of variance ANOVA which compares multiple means If the hypotheses involve two means state the hypotheses in terms of both and 1 2 If the hypotheses involve two proportions state them in terms of both p and p p1 p 2 If the hypotheses involve two standard deviations or variances state them in terms of both 2 and 12 22 or 22 12 All the questions involve means medians proportions or variances One of these problems is a chi squared test Note Look at 252thngs 252thngs on the syllabus supplement part of the website before you start and before you take exams Neatness and clarity of explanation are expected Note that from now on neatness means paper neatly trimmed on the left side if it has been torn multiple pages stapled and paper written on only one side Example This may seem long but it appears on a previous graded assignment 3 A group of supervisors are given exams on management skills before and after taking a course in management Scores are as follows Supervisor Before After 1 63 78 2 93 92 3 84 91 4 72 80 5 65 69 6 72 85 7 91 99 8 84 82 9 71 81 10 80 87 11 68 93 If we assume that the distribution of results is Normal what method should we use to answer the question Has the course improved the scores of the managers What are our hypotheses Solution You are comparing means before and after the course You can get away with using means because the parent distributions are Normal If 2 is the mean of the second sample you are hoping that 2 1 which because it contains no equality is an alternate hypothesis So your hypotheses are H 0 1 2 H 0 1 2 0 or If H 1 1 2 H 1 1 2 0 D 1 2 then H 0 D 0 The important thing to notice H1 D 0 here is that the data are in before and after pairs so you use Method D4 1 West Chester University plays 11 football games a year Though it is a questionable practice these 11 games can be regarded as a random sample taken from an infinite number of games that they might have played Statistics can be computed from them like proportion of games won or the mean and standard deviation of touchdowns or completed passes per game At Christmas 2007 you look at these statistics and assert that the team did significantly better in 2007 than it did in 2006 a The statistic you wish to use is completed passes If x1 is a column listing the number of passes completed in each game in 2006 in random order and x 2 is a column listing the number of passes completed in each game in 2007 in random order and you consider these as independent random samples and wish to compare the mean passes completed per game and to get results that verify your statement what are your hypotheses What is your method b Your roommate Gigglebutz says that you have done this all wrong because the distributions have not been shown to be Normal You do the test described in section 6 3 of the text and sadly agree with Gigglebutz that the distributions are probably not Normal What is your test and method now c Gigglebutz is still not satisfied and points out that these are not independent random samples and what you should do is rearrange all your data so that each column represents a year and each row an opponent Any school that was not played in both years should be dropped from your data What is your test and method now 2 Standard deviation is often a measure of reliability A manufacturer is providing a connector and is getting complaints that the connector is often too large or too small for the intended use A sample of 250 connectors produced by the process in current use is taken Then a new process is tried and a sample of 45 connectors is taken Find the hypotheses and method to show that the new process produces a more reliable product 3 Dummeldinger pg 148 We are interested in attitudes about sexual discrimination Various groups were asked if they believed sexual discrimination is a problem in the United States 05 a Out of 50 men 11 believed that sexual discrimination is a problem Out of 40 women 19 said that sexual discrimination is a problem Is there a significant difference between male and female attitudes b A group of 100 men are picked from upper levels of a group of large American firms They are asked if sexual discrimination is a problem in the United States 38 said yes They are then sent to a program on mentoring female executives where they discuss among other things what problems seem to be peculiar to young female executives Afterwards the men are asked the same question This time 41 said yes Assuming that these 100 men are representative of all exectutives who are trained to mentor female executioves has the training increased the proportion that believe there is a problem c Random samples each 100 people of male 1 high school gradutes 2 college graduates and 3 peple with MBAs are asked the same question Out of the first group 35 said yes Out of the second group 38 said yes Out of the third group 39 said yes Is there a significant difference between the attitudes of the three groups Extra credit Place answers at the end of the assignment d You have enough information to do two of the three problems above What additional information do you need e Do one of the three problems State your conclusion clearly 2 4 Dummeldinger A researcher a random sample of n graduates of MBA programs which included n1 women and n 2 men Their starting salaries were recorded Use 1 and or 1 for population parameters for women and 2 and or 2 for women Choose hypotheses and methods for the following 10 a n1 n 2 150 The researcher wants to show that men have a higher mean starting salary than women b n1 18 and n 2 12 The researcher wants to compare the dispersion of men s and women s salaries The researcher has no prior opinion as to which is more variable c n1 18 and n 2 12 and the null hypothesis in 4b has not been rejected Dummeldinger gives the following data x1 48266 70 and x 2 55000 0 …
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