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Show all your work for each step. Hours of studying based on Scores for the exam Hours 0 2 4 5 5 5 6 7 X Scores 40 51 64 69 73 75 93 90 95 a.) Find the slope m = b.) Find the y-intercept b = c.) Write the equation of the line d.) Determine the correlation constant r = Based on this value do you have confidence in your equation above? e.) What score would you expect if you studied for 3 hours, 6.5 hours, or 4.5 hours? f.) How long would you have to study to ensure a grade of 85? g.) Now find the residual vs. x graph. Show the residuals from the chart first. h.) Find the mean and standard deviation for the sample scores above. i.) Construct a 95% confidence interval estimate around the mean scores. Assume the population data to be normal. j.) Construct a 90% confidence interval estimate around the variance and standard deviation. Definitely show the chi squares that come from the table and the formula's. k.) The standard deviation and mean are from samples but for this problem and the next treat them as if they are population parameters for a normally distributed population, and find the probability of getting a score that is 80 and above. j.) Now find a 95% confidence interval estimate around the mean, with the idea that this is a population parameter for a normally distributed population