At a 5% significance level, for which of the following p-values of a test…
2023
At a 5% significance level, for which of the following p-values of a test statistic is the null hypothesis likely to be accepted (that is, not rejected)?
A. 0.32 of 2%
B. 32%
C. 2%
D. 0.42
Choose the correct answer from the options given below:
Answer: C. B and D only — ConceptA p-value measures how compatible the observed data are with the null hypothesis. At significance level α, reject the null hypothesis when p ≤ α; when…
- A.
A and B only
- B.
B and C only
- C.
B and D only
- D.
A and C only
Show answer & explanation
Correct answer: C
Concept
A p-value measures how compatible the observed data are with the null hypothesis. At significance level α, reject the null hypothesis when p ≤ α; when p > α, fail to reject it.
Thus, at the stated 5% level, p-values above 0.05 support the question’s wording “likely to be accepted,” meaning not rejected.
Application
Set the stated significance level to α = 0.05.
Convert every listed value to decimal form, taking “of” as multiplication.
Compare each decimal p-value with 0.05 and apply the decision rule.
Select the pair whose two members both lead to failure to reject the null hypothesis.
Statement | Decimal p-value | Relation to 0.05 | Test decision |
|---|---|---|---|
A: 0.32 of 2% | 0.32 × 0.02 = 0.0064 | Below 0.05 | Reject the null hypothesis |
B: 32% | 0.32 | Above 0.05 | Fail to reject the null hypothesis |
C: 2% | 0.02 | Below 0.05 | Reject the null hypothesis |
D: 0.42 | 0.42 | Above 0.05 | Fail to reject the null hypothesis |
Cross-check
The larger values 0.32 and 0.42 provide weaker evidence against the null hypothesis.
The smaller values 0.0064 and 0.02 provide stronger evidence against the null hypothesis at the 5% level.
Result
The required pair is B and D only.