Question

(c) Figure the correlation coefficient. r= (Round to two decimal places as needed.) (d) Give three logically possible directions of causality, saying for each whether it is a reasonable direction in light of the variables involved. Select all that apply. A. It could be that higher test scores cause longer study times. This is not a reasonable direction of causality, as the tests would have been graded after study time. B. It could be that longer study times cause higher test scores. This is not a reasonable direction of causality, as many students do not study without scores to motivate them. C. It could be that both study time and grades influence course subject. This is not a reasonable direction of causality, as the test is about the subject material. D. It could be that course subject influences both study time and grades. This is a reasonable direction of causality, as students may focus more on subjects they prefer. E. It could be that higher test scores cause longer study times. This is a reasonable direction of causality, as higher test scores motivate students to study more. OF. It could be that longer study times cause higher test scores. This is a reasonable direction of causality, as students that study more likely retain more knowledge.

Answer 1

c)

r = 0.83.

The provided data are shown in the table below х Y 0 53 10 94 6 81 9 72 6 66 Also, the following calculations are needed to com ite the correlation coefficient: X Y X*Y X2 y2 0 53 0 0 2809 10 94 940 100 8836 6 81 486 36 6561 9 72 648 81 5184 6 66 396 36 4356 Sum = 31 366 2470 253 27746 The correlation coefficient r is computed using the following expression: r = SSXY VSSxx SSyy where SSXY 2 n 1 Σκη - (Σκ) (Σ) Skaz x 3 () ΣΧ; n 2 SSyy = Y? In this case, based on the data provided, we get that 1 SSXY = 2470 (31 (31 x 366) = 200.8 5 1 SSxx 253 (31)2 = 60.8 SSYY = 27746 $(366)2 = (366)2 = 954.8 Therefore, based on this information, the sample correlation coefficient is computed as follows r = SSXY VSSxx SSyy 200.8 V 60.8 x 954.8 0.833

d)

Options

A, C and D are correct.

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