252grass3 052 10 25 05 Open this document in Page Layout view Name Class days and time Please include this on what you hand in Graded Assignment 3 A 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 If the hypotheses involve a mean state the hypotheses in terms of both and 1 2 If the hypotheses involve a proportion state them in terms of both p and p p1 p 2 If the hypotheses involve 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 Remember that a yes answer is not acceptable without an explanation Note Look at 252thngs 252thngs on the syllabus supplement part of the website before you start and before you take exams Remember that I use and p as parameters and x s x 50 x as sample statistics n Example This may seem long but it appears on an old Graded Assignment 3 A group of supervisors are given the 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 and p 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 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 You have data on income in two villages x1 in village 1 x 2 in village 2 You want to test the hypothesis that village 2 has higher earnings than village 1 You know that income has an extremely skewed distribution and you have to decide whether to use the mean or the median income 2 The data in the file CONCRETE 1 on your CD represents the strength measured by how many thousands of pounds square inches that they can take without buckling of 40 concrete samples on the second and seventh days after pouring x1 is the strength on the second day and x 2 is the strength on the seventh day each line refers to a single sample Assume that the underlying distribution is Normal and test the hypothesis that it is stronger on the seventh day 3 You have interviewed a sample of 80 small businesses in the Northeast and 75 small businesses in the Southeast Each business has indicated whether they sell in foreign markets You want to show that businesses in the Northeast are more likely to export x1 is the total number of firms that export in the Northeast sample x 2 in the Southeast 4 You expand the sample in 3 by adding 60 small businesses in the Midwest x 3 is the number of these that export You test the hypothesis that the same fraction of businesses export in each region 6 In order to see which garage to use under contract for automobile repairs 10 cars are towed first to garage 1 and than to garage 2 You end up with two data sets the first data column x1 is estimates from the first garage and the second data column x 2 is estimates for the second garage Each of the 10 lines of data refers to one car You believe that the estimates are approximately normally distributed Compare the estimates in garage 1 and 2 Would you change your method if there were 200 cars 7 You have processing times in seconds x1 for a sample of 5 computer jobs from the accounting department and for 6 jobs from the research department x 2 You believe that the underlying distributions are Normal and want to show that research jobs take longer than accounting jobs Would you change your method if n1 n 2 205 8 You are having a part produced in two different machines x1 is 200 randomly selected data points that represent the length of parts from machine one x 2 is 200 randomly selected data points that represent the length of parts from machine two You want to test your suspicion that parts from machine 2 are longer than parts from machine 1 In a problem of this type you would assume that the lengths are normally distributed 9 You also suspect that parts from machine two are more variable in length than parts from machine one This is the same as saying that machine 2 is less reliable than machine 1 Test this suspicion 10 A panel is exposed to an ad for Smelly Welly Dirt Devourer Before seeing the ad 5 out of the 40 members had a favorable impression of Smelly Welly After seeing the ad 2 more members of the panel plus the original 5 had a favorable impression Has the proportion with favorable impressions risen significantly B You have 3 methods that can be used for goodness of fit tests Chi squared Kolmogorov Smirnov and Lilliefors Which would you use in the following cases 1 You want to know if the Normal distribution applies to a data set a The data set consists of 15 numbers you do not know the population mean and variance and will have to compute sample means and variances from the data b The data set consists of 15 numbers you think that you know the population mean and variance c The data set consists of 5000 numbers and you have observed frequencies for the following intervals below 1000 1000 11199 99 1200 1399 99 1400 1599 99 2600 2799 99 2800 and above You think you know the population mean and variance d The data set consists of 5000 numbers and you have observed frequencies for the following intervals below 1000 1000 11199 99 1200 1399 99 1400 1599 99 2600 2799 99 2800 and above You have computed a sample mean and variance from the data 2
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