Question: statistics questions. I do not have much time. could you be fast. I got 25 minutes You have three marketing personnel in your company. They

statistics questions. I do not have much time. could you be fast. I got 25 minutes

You have three marketing personnel in your company. They are David, Marie and James. Their performance in last 10 month period is your concern. Below you will find the related data and some graphs. Then you will answer the questions. Personnel 1 2 3 4 5 6 17 8 9 10 David 13 11 12 16 17 16 19 18 22 26 Marie 15 20 17 23 17 19 12 15 19 23 James 10 11 10 15 15 17 16 16 19 21 On a graph, their performance looks like this; 30 25 20 15 10 UT 10 12 David +Marie --James Firstly you carried out individual simple linear regressions with respect to time for these three. The regression outputs and other related sample information are given in the table below; David Marie James Sample arithmetic mean 17 18 15 Sample variance 21.1 12.4 13.8 Regression Results Correlation coefficient 0.93 0.13 0.94 Intercept (a) 6 17.2 8.67 Slope (b) 1.41 0.15 1.15 Std. error of the slope 0.20 0.41 0.15 QUESTIONS (First six questions are 10pt each, last two questions are 20pt each) 1- Using proper statistical tests, compare if the correlations between David-Time and Marie-Time bivariate relationships are equal at a 95% confidence level. (Test Ho: PDavid = PMarie) 2- Test the equality of regression slopes for David and James at a 95% confidence level. (Test Ho: David = Pjames) 3- If you would have to fire one of these guys, who would you fire and why? 4- The sales/interviews ratios for your three personnel are (170/473, 180/537, 150/496) respectively. Test whether the sales proportion of Marie is higher than James. (Test Ho: PMarie S Pjames) 5- Test the equality of variances between David and Marie at a 95% confidence level. (Test Ho: "David = Marie) 6- Test the equality of arithmetic means between David and Marie at a 95% confidence level. (Test Ho: HDavid = HMarie) 7- Test the equality of arithmetic means between all three guys at a 95% confidence level. (Carry out an analysis of variance. SST=472.67) 8- Suppose only for this question you know the population standard deviation of James. It is james = 15. For a hypothesis test of Ho: Hjames 2 17 at a 95% confidence level where HReal = 15, find the power of the test

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