Question

a survey was taken comparing the number of hours per week students spent watching tv and their performance on an exam. if a linear regression was performed and the correlation coefficient was -0.974, what can be said about these results? there is little evidence of a linear relationship between the number of hours spent watching tv and student exam performances. as the number of hours spent watching tv increases, student exam performances will likely not change. as the number of hours spent watching tv increases, student exam performances will probably decrease. as the number of hours spent watching tv increases, student exam performances will probably increase.

Explanation:

The correlation coefficient \( r = -0.974 \) is close to -1, indicating a strong negative linear relationship. A negative correlation means that as one variable (hours watching TV) increases, the other (exam performance) tends to decrease. The first option is wrong because \( |r| \) is close to 1, so there is strong evidence. The second option is wrong as the correlation is not near 0 (no linear relationship). The fourth option is wrong because the correlation is negative, not positive. So the correct interpretation is that as TV - watching hours increase, exam performance likely decreases.

Answer:

As the number of hours spent watching TV increases, student exam performances will probably decrease