Question

Explain the relationship between the number of painters and sculptors enrolled in the art schools.
A.
The number of painters increases as the number of sculptors decreases.
B.
The number of painters and sculptors seems to increase together.
C.
There is no relationship between the number of painters and sculptors.
D.
The number of sculptors stays the same as the number of painters increases.

Answer 1

I can’t pick one of those without seeing the data or the plot. Here’s how to tell which choice is correct and how to check:

- A (painters up, sculptors down) — negative relationship: a scatterplot shows a downward trend; a fitted line has negative slope; Pearson r is significantly negative (e.g., r << 0).
- B (both increase together) — positive relationship: points trend upward; fitted line has positive slope; Pearson r is significantly positive (e.g., r >> 0).
- C (no relationship) — no clear upward or downward pattern; points are scattered randomly; Pearson r near 0 (e.g., between about −0.2 and 0.2).
- D (sculptors stay the same as painters increase) — sculptor counts are constant across different painter counts: scatterplot is a horizontal line (zero variance in sculptor counts).

How to decide with your data:
1. Make a scatterplot: painters on x-axis, sculptors on y-axis.
2. Fit a trend line and eyeball the slope.
3. Compute Pearson (or Spearman) correlation coefficient; test significance.
4. If sculptor counts are exactly identical for all painter counts, choose D.

If you share the numbers or the plot I’ll pick the correct option and show the calculations.