STAT200 Week 7 Homework This is the last homework in our class Problem 1. For the X,Y data in the table, compute the coefficient of correlation r. x y 5 2 10 12 22 15 28 24 40 42 x y xy Show work Problem 2. For the (X, Y) data in the table, compute slope and y-intercept of the regression line. X Y 4 8 7 10 13 18 16 20 Show work Problem 3. (2points) Table below shows results for 10 selected students on Test-1 and Test-2: Test-1 Test-2 Difference 1 2 3 4 5 6 7 8 9 10 86 75 68 94 95 82 65 95 86 77 79 77 70 98 100 85 70 100 92 82 You should use Hypothesis Testing technique to evaluate Null Hypothesis: Ho: there is no significant differences between mean score on Test-1 and Test-2. Use significance level = 0.10. Here are steps to follow: a) Calculate difference of scores for each student. b) Find Mean (M) and Sample Standard Deviation (s) for values in the column Difference. c) Find Standard Error of Mean sm = s/N . d) Calculate t-value as t = M/sm e) Use Excel function TDIST(t, df,2) to find p-value (df = N-1). f) Compare p-value with the given significance level 0.10. If p-value is less than 0.10 then reject Ho. If p-value is greater than 0.10 accept Ho. Show work Question 4. Table below shows number of students who failed different math courses in Spring (Expected Frequency) and in Fall (Observed Frequency) semesters: Course Spring Expected Fall Observed (E - O)2 (E - O)2/E College Algebra Statistics Calculus-I Calculus-II (E) Frequency 10 14 16 7 (O) Frequency 12 16 13 9 Null Hypothesis Ho: distribution of failed students is the same in Spring and Fall semesters. Use Chi-Square test with the significance level 0.10 to check if given data support or do not support Ho (should we reject or do not reject Ho). a) Calculate Chi Square (sum of the last column). b) Use Excel function =CHIDIST(Chi-Square, df) to find p-value for this case. c) Compare p-value with the significance level 0.10. If p-value is less than 0.10 then reject Ho. If p-value is greater than 0.10 then do not reject (accept) Ho. Show work