SAS ON Demand take-home test on SAS-on deman

weeks chlorine 8 0.46 8 0.5 10 0.48 10 0.47 10 0.49 10 0.47 12 0.46 12 0.45 12 0.46 14 0.44 14 0.43 14 0.43 16 0.43 16 0.42 18 0.45 18 0.44 20 0.42 20 0.42 20 0.43 20 0.41 22 0.42 22 0.41 22 0.4 24 0.43 24 0.4 24 0.4 26 0.4 26 0.41 28 0.41 28 0.39 30 0.4 30 0.4 30 0.39 32 0.41 32 0.4 34 0.4 36 0.39 36 0.36 38 0.35 38 0.37 40 0.36 42 0.35

1 0 1 1 1 1 2.8 1.0 0.4 1 0 1 1 0 2 1.0 0.4 0.7 1 0 1 0 1 3 3.0 1.2 0.7 1 0 1 0 0 4 1.5 0.9 1.0 1 1 1 1 1 5 3.0 0.6 0.6 1 1 1 1 0 6 2.1 0.5 0.8 1 1 1 0 1 7 2.9 1.1 0.9 1 1 1 0 0 8 2.1 0.9 0.7 2 0 1 1 1 9 6.8 6.8 1.0 2 0 1 1 0 10 5.4 6.1 0.2 2 0 1 0 1 11 6.5 7.3 1.3 2 0 1 0 0 12 5.4 6.4 0.7 2 1 1 1 1 13 2.9 2.2 1.1 2 1 1 1 0 14 2.8 2.3 0.8 2 1 1 0 1 15 3.6 2.6 0.3 2 1 1 0 0 16 3.0 2.5 0.4 1 0 3 1 1 1 3.5 0.9 0.8 1 0 3 1 0 2 1.4 0.3 0.9 1 0 3 0 1 3 3.7 1.1 0.4 1 0 3 0 0 4 1.8 0.7 0.6 1 1 3 1 1 5 3.5 0.5 0.8 1 1 3 1 0 6 2.3 0.5 0.8 1 1 3 0 1 7 3.5 1.1 1.6 1 1 3 0 0 8 2.2 0.8 0.6 2 0 3 1 1 9 7.9 7.3 1.2 2 0 3 1 0 10 7.0 6.5 1.3 2 0 3 0 1 11 8.0 7.8 0.8 2 0 3 0 0 12 7.2 6.9 0.9 2 1 3 1 1 13 4.0 2.8 0.5 2 1 3 1 0 14 4.2 3.0 0.7 2 1 3 0 1 15 4.8 3.0 0.4 2 1 3 0 0 16 4.5 3.3 0.9 1 0 5 1 1 1 4.0 0.9 0.9 1 0 5 1 0 2 1.8 0.4 0.7 1 0 5 0 1 3 4.2 1.1 0.8 1 0 5 0 0 4 1.9 0.5 0.9 1 1 5 1 1 5 3.9 0.7 0.9 1 1 5 1 0 6 2.5 0.5 0.5 1 1 5 0 1 7 3.7 1.0 1.1 1 1 5 0 0 8 2.2 0.6 1.1 2 0 5 1 1 9 8.6 7.0 0.7 2 0 5 1 0 10 7.5 6.7 0.5 2 0 5 0 1 11 8.8 7.6 0.6 2 0 5 0 0 12 7.9 7.1 1.1 2 1 5 1 1 13 4.7 3.1 1.1 2 1 5 1 0 14 4.8 3.2 0.5 2 1 5 0 1 15 5.3 3.5 0.3 2 1 5 0 0 16 5.2 3.4 0.5

Description: Length and Width Shrinkage and Skewness Measurements for a 5 factor experiment varying structure, presence of wrinkle resistant finish, cycle number, rinse cycle softener, and drying method. Variables/columns Structure 8 /* 1=Poplin, 2=Sheeting */ Wrinkle resistant finish 16 /* 0=No, 1=Yes */ Cycle Number 24 Rinse Cycle Softener 32 /* 0=No, 1=Yes */ Drying Method 40 /* 1=Tumble Dry, 0=Line Dry */ Specimen Number 47-48 /* Presumably */ Length Shrinkage Percent 54-56 Width Shrinkage Percent 62-64 Skewness Percent 70-72

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STAT 303 Take Home Test Directions: 1) You are expected to work alone on this Take Home Test. You may use your textbook, any SAS book or website, or any textbook or website on statistics. The only human you may speak with about this test is. 2) The test must be uploaded to SAKAI on or before 11:55 PM on December 2. Late tests will not be accepted. 3) You should include your code and any important output with your test. You may write one piece of continuous code for each problem. Every graph should include an appropriate title. 4) Sign the honor pledge in Sakai. Grading: 1) You will be graded on accuracy of the code as well as efficiency of the code. 2) You will be graded on your statistical analysis of the data and accuracy of your interpretations. Make sure you answer EVERY problem asked and that whoever grades your test can find the answers easily. 3) You will be graded on the output. Points will be deducted for superfluous output. Only include the output necessary to support your conclusions. 4) If you cannot perform a data step (like opening files or using do-loops) you may copy the data out of the file or into a format you can manage so you can analyze the statistics. However, there will be deductions for doing this. There are three questions. Be sure you read and complete all of them. 1. The text file chlorine.txt is a tab delimited file that contains two variables in the header row: chlorine and weeks. The variable chlorine is the proportion of chlorine available in a certain product and we are measuring it over time in weeks. a) (2 pt) Read the data in using SAS commands. b) (3 pt) Perform a correlation on chlorine and weeks. Include the scatter plot from Proc Corr using the plots option. Does the relationship seem strong and linear? c) (2 pt for code) Perform a linear regression on the data. Analyze the output (i) (2 pt) State the r-square value and interpret what it means. (ii) (2 pt) Perform a hypothesis test on the parameter for weeks to test the significance of the slope parameter. State the null and alternative hypothesis. State the test statistic and p-value. Is the parameter estimate of the slope significant at α 0.05. (iii) (1 pt) State the equation to predict the proportion of chlorine as a function of weeks. (iv) (2 pt) Analyze the residual plots for adequacy of the assumptions, outliers and leverage points. Discuss any violations. d) You should find that the linear model is not adequate. (i) (2 pt) It is possible the model is an exponential decay. Include the natural log of chlorine in the data step and generate the linear model of the natural log of chlorine vs weeks. (a) (1 pt) State the R-sq (b) (2 pt) Assess the residual assumptions. (c) (1 pt) Does this appear to be a reasonable model? (ii) (2 pt) It is possible the model is a reciprocal model. Include the reciprocal of chlorine in the data step. and generate the linear model of the reciprocal of chlorine vs weeks. (a) (1 pt) State the R-sq (b) (2 pt) Assess the residual assumptions. (c) (1 pt) Does this appear to be a reasonable model? (iii) (3 pt) Out of these two models, which is the best? Create the scatter plot of the data with the actual model overlaid using Proc Gplot or Proc Sgplot. e) (2 pt) Using Proc Loess, write the following code which allows you to see the trend between chlorine and weeks. Proc Loess data = ; model = ; run; You should see a cubic might be a potential candidate for the model. f) (3 pt) Create a cubic model to predict chlorine from weeks. You need to include the linear, quadratic and cubic terms in the model. Include the scatter plot with the model using the plots command in Proc Reg. (a) (1 pt) State the R-sq (b) (2 pt) Assess the residual assumptions. (c) (1 pt) Does this appear to be better than the model you choose as the best model in part d)? 2. The excel file OpinionPoll.xlsx contains data from an opinion poll on raising the minimum wage to $15 per hour based on sex and political party affiliation. The data is found in column one of the Excel file as two letters and a number where the first letter represents the sex of the person, the second letter is the party affiliation and the last character represents the person's opinion. The data looks like Sex | Party |Opinion FR2 MR2 FD1 a. (2 pt) Create formats for the three variables where Sex: M = Male, F = Female Party: D = Democrat, O = Other, R = Republican Opinion: 1 = For, 2 = Against. b. (2 pt) Import the data. c. (3 pt) In a new data set separate the data using the substr() command. Associate the formats in this data set. d. (2 pt) Create a side-by-side vertical bar chart where opinions are side-by-side grouped by sex. Describe any statistical relationships you see or don't see. e. (2 pt code) Perform a Chi-square to determine if there is a difference in raising the minimum wage to $15 per hour by sex. In your table only include the frequency, expected value, row percent and column percent. 1) (1 pt) State your null and alternative hypothesis 2) (2 pt) State the test statistic, p-value and conclusion at a significance level of 0.05. f. (2 pt) Create a side-by-side vertical bar chart of opinions grouped by party affiliation. Define the order of the grouped axis to be in the order of Democrats, Republicans, Other (you will need to change the order). Order the main axis as "For" followed by "Against". Use the "gaxis = " command to order the group variable and the maxis = for the midpoint/main axis. Describe what you see. g. (2 pt code) Perform a Chi-square to determine if there is a difference in opinion based on party affiliation. In your table only include the frequency, expected value, row percent and column percent. 1) (1 pt) State your null and alternative hypothesis 2) (2 pt) State the test statistic, p-value and conclusion at a significance level of 0.05. h. Let's explore the relationship of opinion and sex separated by party affiliation. 1) (1 pt) Sort the data by party affiliation. 2) (2 pt) Create a frequency table and Chi-square test for opinion and sex for each party affiliation. You should use the "By" statement in Proc Freq to help achieve this. In your table only include the frequency, expected value, row percent and column percent. Include the odds ratio for each table. 3) (1 pt) For Democrats is there is a difference in opinion based on sex? State the statistics that help you determine this. Test at α=0.05 for this and the next two questions. 4) (1 pt) For Others is there is a difference in opinion based on sex? State the statistics that help you determine this. 5) (1 pt) For Republicans is there is a difference in opinion based on sex? State the statistics that help you determine this. 6) (2 pt) State the odds ratio of females supporting the $15 per hour wage compared to males for those who identify as Other. Interpret this. 7) (1 pt) Based on these results, is there a difference in opinion based sex controlling for party affiliation. i. (1 pt) This exercise demonstrates Simpson's Paradox. Do some research on Simpson’s Paradox and explain how this example demonstrates this. 3. The file laundrydesc.txt describes the data in the file laundry.txt. a.(2 pt) Create appropriate formats using the descriptions of the variables in the file laundrydesc.txt for the variables structure, wrinkle resistant finish (Use Not Resistant =0 and Resistant = 1 ) , and drying method. b. (3 pt) Use SAS to import the data for laundry.txt. Create your variables and create labels that describe the variables based on the descriptions in laundrydesc.txt. Apply the formats created in previous step to the respective variables in this data step. c. (2 pt) Using proc means calculate the mean, standard deviation, skewness, max and min of the three response variables (length shrinkage percent, width shrinkage percent, and skew percentage) for the categories of structure, wrinkle resistant finish and drying method. d. Create one side-by -side plot of the structure, wrinkle resistant finish and drying method for all three response variables as seen below. In order to put this on one plot, you will need to use do-loops (i) Create a new data set to read in the data from the original data. (ii) Use an array to group the three response variables of length shrinkage percent, width shrinkage percent and skew percentage. (iii) Use a do-loop to (a) Create a variable that stores the shrink percentage from your array. (b) Using if statements assign a variable type to assign the type of shrinkage being measured (length, width or skew) (iv) (3 pt to restructure the data) Use your new data to create three vertical bar charts. (a) (2 pt) One for the structure with every type of shrink percentage. The y-axis should display the mean shrink percentage. Describe what you see statistically in the graph. Your graph should look like the graph above with structure on the x-axis grouped by the different shrinkage variables. (colors optional) (b) (1 pt) One for the wrinkle resistant finish status with every type of shrink percentage. The y-axis should display the mean shrink percentage. Describe what you see statistically in the graph. (c) (1 pt) One for the drying method with every type of shrink percentage. The y- axis should display the mean shrink percentage. Describe what you see statistically in the graph. (Note, I was able to do this with do-loops. There may be other methods aside from inputting the data by hand. If you can dream up a different method that use other SAS coding methods aside from inputting by hand, that is valid. If you cannot do this, give me three separate graphs for each category for partial credit. You will have 9 total bar charts.) e. (3 pt for code) Using Proc Ttest, compare the mean of the length shrinkage percent, width shrinkage percent and skew percentage between the wrinkle resistant finish type. (Three different t-tests) (1) (1 pt) State the null and alternative hypothesis in general (just say shrinkage based on type or something like this for the different shrinkage measurements.) (2) (6 pt) State the test statistic, p-value, conclusion at α = 0.02 for each of the tests. Evaluate the validity of the test. Be sure to indicate if you use the pooled or Satterthwaite test statistic and p-value and why. (3) (2 pt) State the 98% confidence interval of the difference in means of the difference in width shrinkage percent (only) based on wrinkle resistant categories and interpret. f. (2 pt code)Perform an Analysis of Variance test (ANOVA) to compare the width shrinkage percent for structure and wrinkle resistant finish status as one model. (1) (1 pt) State the null and alternative hypothesis. (2) (2 pt) State the test statistic, p-value, conclusion at α = 0.02 for each variable.