3. A researcher is investigating the relationship between the number of hours spent studying and the...

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3. A researcher is investigating the relationship between the number of hours spent studying and the final exam score for a group of 20 students in a statistics class. The data for the number of hours spent studying (X) and the corresponding final exam score (Y) are as in Table 2. Table 2 Student Hours of Study Final Exam Score 1 10 60 2 15 65 3 20 70 4 25 75 5 30 78 6 35 80 7 40 85 8 45 87 9 50 88 10 55 85 11 60 87 12 65 88 13 70 90 14 75 92 15 80 92 16 85 94 17 90 95 18 95 96 19 100 97 20 105 98 (a) Calculate the Pearson correlation coefficient between the number of hours spent studying and the final exam score. (12) (b) Test the hypothesis at a significance level of 0.05 to determine if there is a significant linear relationship between the two variables. (8) 3. A researcher is investigating the relationship between the number of hours spent studying and the final exam score for a group of 20 students in a statistics class. The data for the number of hours spent studying (X) and the corresponding final exam score (Y) are as in Table 2. Table 2 Student Hours of Study Final Exam Score 1 10 60 2 15 65 3 20 70 4 25 75 5 30 78 6 35 80 7 40 85 8 45 87 9 50 88 10 55 85 11 60 87 12 65 88 13 70 90 14 75 92 15 80 92 16 85 94 17 90 95 18 95 96 19 100 97 20 105 98 (a) Calculate the Pearson correlation coefficient between the number of hours spent studying and the final exam score. (12) (b) Test the hypothesis at a significance level of 0.05 to determine if there is a significant linear relationship between the two variables. (8)