OBSEVATIONS Attribute Name 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 X = Crime Rate 28.5 54.3 34.7 60.3 62.5 61.9 30.4 39.3 50.1 62.4 61.8 36.3 21.8 38.8 36.9 43 53.9 62 41 39.5 54.2 62.8 21.9 33 45.7 62.1 47.5 20.6 40.4 31.1 39 35.9 14.6 15.7 14.9 14.1 13.6 27.6 13.9 15.3 61.8 47 60.9 33.9 21.8 Y = Sale Price (Divided by 1,000) 4,500 1,225 1,450 1,750 2,000 999 2,350 1,915 4,250 970 490 2,000 3,295 3,550 1,550 1,290 1,100 841 1,200 1,159 748 650 4,600 1,054 975 Z = Miles From Downtown 11 12.7 10.2 15.4 13 16.4 14.3 19.1 17.9 18.3 12.2 13.5 11.6 9.7 15.9 18.7 2 PROBLEMS Problem 1 (0 points) Use your XYZ data to compute the following parameters and use these parameters in the remaining problems, as required. You do not need to show work and you may use, calculator, Excel, or Minitab for this question. 39.30444 a) Compute mean of X Xm = b) Compute standard deviation of X Xs = 16.59195 c) Compute Xt, where Xt = Xm*0.97 Xt = 38.12531111 d) Compute mean of Y Ym = 1,836.44 e) Compute standard deviation of Y Ys = 1232.617 f) Yw = 36.7288 Compute Yw, where Yw = Ym*0.02 g) Compute mean of Z Zm =14.36875 h) Compute standard deviation of Z Zs = 3.108208219 i) Zt =15.0871875 Compute Zt, where Zt = Zm*1.05 3 Problem 2 (5 points) a) Use Minitab to determine the probability distribution type of X, attach the chart, and explain how you determined the best distribution type. 4 Problem 3 (5 points) a) Use Excel to determine a [nonlinear] function for X, based on the probability distribution in the previous problem (or a reasonable approximation). b) Compute and state your confidence in this function. Attach the chart and show the function and any measure of confidence 5 Problem 4 (10 points) Sort the Z observations in ascending order, and assume the following probabilities for the sorted observations: p(z) = [.01, .03, .04, .05, .07, .09, .10, .13, .12, .11, .08, .07, .04, .03, .02, .01] Assume h(z) = W = aZ + b as you determined in the previous problem. a) What is the expected value of the function h(x)? (Feel free to use the abbreviated computation we discussed in class). b) What are the variance and standard deviation of the function h(z)? (Feel free to use the abbreviated computation we discussed in class). c) What does the variance tell you about the expected value of the function? 6 Problem 5 (15 points) Assuming Y has a normal distribution (CLT is used) a) What is the confidence interval for the mean of Y using a confidence level of 90%? b) What is the prediction interval for the mean of Y using a confidence level of 90%? c) Explain the difference between the above confidence interval and prediction interval. 7 Problem 6 (5 points) Assume a target confidence interval w = Yw. What sample size of Y is required to obtain w using a 90% confidence level, as in the above problem? 8 Problem 7 (10 points) Assume X, in your project, is concerned with a one-sided confidence interval. What is the upper confidence bound for the true average of X with a confidence level of 95%? Provide an explanation of the result in the context of your project. 9 Problem 8 (15 points) Using the context of X in your project: a) b) c) d) State a hypothesis about the true average being less than Xt Select a significance level of your choice Manually test the hypothesis Explain the outcome. 10 Problem 9 (15 points) Using the context of Z in your project: a) b) c) d) State a hypothesis about the true average being equal to Zt Let significance level = 0.01 Manually test the hypothesis Explain the outcome. 11 Problem 10 (20 points) Sort X and Y and pair the Y with the first 25 observations of X. Assume these data points are paired data from the same subjects (disregard the context of X and Y in the project). a) b) c) d) State a reasonable hypothesis about the paired data Let significance level = 0.01 Manually test the hypothesis Explain the outcome 12
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