Question

based on the data, which inference is valid?
a. time spent studying has no effect on a test score.
b. there is a positive correlation between study time and test scores.
c. a student who studies 20 minutes will definitely pass the test.
d. there is a negative relationship between study time and test scores.
(scatter plot with test score on x - axis (50 - 100) and time spent studying (min) on y - axis (0 - 50), with a negative trend line and data points)

Explanation:

Step1: Analyze Option A

Option A claims time spent studying has no effect on test score. But the scatter plot has a trend (the line of best fit), so there is an effect. Eliminate A.

Step2: Analyze Option B

The line of best fit has a negative slope (as study time increases, test score decreases), so it's a negative correlation, not positive. Eliminate B.

Step3: Analyze Option C

A student studying 20 minutes: The line of best fit at 20 minutes study time doesn't guarantee passing (passing score not defined, and scatter points vary). Eliminate C.

Step4: Analyze Option D

The scatter plot and line of best fit show as study time (x - axis) increases, test score (y - axis) decreases, so there's a negative relationship. This is valid.

Answer:

D. There is a negative relationship between study time and test scores.