A researcher computes sample correlation coefficients r1, r2, r3, and r4 from…
2023
A researcher computes sample correlation coefficients r1, r2, r3, and r4 from four different samples and obtains their p-values as 0.99, 0.999, 0.05, and 0.005, respectively. Which correlation coefficient is significant at the 1% level?
Answer: D. r4 — ConceptIn hypothesis testing, the significance level α is the maximum probability of a Type I error accepted in advance. A result is statistically significant…
- A.
r1
- B.
r2
- C.
r3
- D.
r4
Show answer & explanation
Correct answer: D
Concept
In hypothesis testing, the significance level α is the maximum probability of a Type I error accepted in advance. A result is statistically significant at level α when its p-value is less than or equal to α.
The p-value is compared directly with α; the numerical size of the correlation coefficient itself is not needed for this decision.
Application
Here the 1% significance level is α = 0.01. Compare each reported p-value with 0.01.
Coefficient | p-value | Multiple of 0.01 | Comparison with α |
|---|---|---|---|
r1 | 0.99 | 99 | Greater than α |
r2 | 0.999 | 99.9 | Greater than α |
r3 | 0.05 | 5 | Greater than α |
r4 | 0.005 | 0.5 | Less than α |
Set α = 1/100 = 0.01.
Apply the decision rule: a coefficient is significant when its p-value is less than or equal to α.
The comparisons show that only 0.005 is less than 0.01.
Cross-check
The other p-values, 0.99, 0.999, and 0.05, are all greater than 0.01, so they do not meet the 1% significance threshold.
Result
The required correlation coefficient is r4.