Question

(a)

The following chart displays the number of hours that 7 students spent studying for their Prob/Stats final exam, along with their final exam scores.





Part A

Using technology, find the correlation coefficient rrr. Enter the value of rrr into the box below, rounded to the nearest hundredth.

(b)

Part B

Describe the type and strength of the correlation – explain your answer using the value of r you found in Part A.



Math

Answer 1

I don't see the chart or the seven (hours, score) data points. Please either paste the seven pairs of numbers or upload an image of the chart, and I'll compute r and give the interpretation.

If you want to compute r yourself, here are quick ways and how to interpret the result.

How to get r using technology
- Excel / Google Sheets: put hours in one column (A2:A8) and scores in the next (B2:B8). Use =CORREL(A2:A8,B2:B8). Round the result to the nearest hundredth.
- TI-84 (or similar): Stat → Edit → enter data in L1 and L2; then Stat → Calc → 8: LinReg(ax+b) (or LinReg(a+bx)); make sure DiagnosticsOn (2nd → 0 → DiagnosticOn) to see r.
- R: use cor(hours, scores) or cor.test(hours, scores).
- Python: import numpy as np; np.corrcoef(hours, scores)[0,1].
- Manual formula:
r = [ Σ(xi - x̄)(yi - ȳ) ] / [ sqrt( Σ(xi - x̄)^2 ) * sqrt( Σ(yi - ȳ)^2 ) ]

How to describe type and strength (use the r you find)
- Type: sign of r -> positive r = positive (as hours increase scores tend to increase); negative r = negative (as hours increase scores tend to decrease).
- Strength (common guideline):
- |r| < 0.3: very weak or negligible
- 0.3 ≤ |r| < 0.5: weak to moderate
- 0.5 ≤ |r| < 0.7: moderate to strong
- |r| ≥ 0.7: strong to very strong
Give your interpretation like: “r = 0.82 (rounded to 0.82) indicates a strong positive linear correlation: students who studied more hours tended to get higher scores.”

Send the data and I’ll compute r and give the exact rounded value and a short interpretation.