A researcher obtains the following p-values for sample correlation…
2023
A researcher obtains the following p-values for sample correlation coefficients of different samples. Which of these can be considered
significant at 1% level of significance?
A.0.004
B. 0.99
C. 0.995
D. 0.001
E.0.1
Choose the correct answer from the options given below:
Answer: C. A & D only — ConceptA p-value measures how compatible the observed result is with the null hypothesis. The significance level α is the decision threshold chosen before…
- A.
B & C only
- B.
B, D & E only
- C.
A & D only
- D.
B, C & E only
Show answer & explanation
Correct answer: C
Concept
A p-value measures how compatible the observed result is with the null hypothesis. The significance level α is the decision threshold chosen before testing.
A result is statistically significant when p ≤ α; smaller p-values provide stronger evidence against the null hypothesis.
Application
Convert the 1% significance level to a decimal: α = 1/100 = 0.01.
Compare A: 0.004 ≤ 0.01, so it is within the rejection region.
Compare B: 0.99 > 0.01, so it is outside the rejection region.
Compare C: 0.995 > 0.01, so it is outside the rejection region.
Compare D: 0.001 ≤ 0.01, so it is within the rejection region.
Compare E: 0.1 > 0.01, so it is outside the rejection region.
Cross-check
Both 0.004 and 0.001 are less than one hundredth, whereas 0.1, 0.99, and 0.995 are greater than one hundredth.
Therefore, the significant p-values are A (0.004) and D (0.001), giving the set “A & D only”.