Suppose you are conducting a test of
𝐻
0
:
𝜇
=
12.0
versus
𝐻
1
:
𝜇
≠
12.0
. After collecting and summarizing sample data, you find that p-value
𝛼
. Which of the following statements represents the correct concluding statement?

Question

Suppose you are conducting a test of 
𝐻
0
:
𝜇
=
12.0
 versus 
𝐻
1
:
𝜇
≠
12.0
. After collecting and summarizing sample data, you find that p-value > 
𝛼
. Which of the following statements represents the correct concluding statement?

BlackTom AI · Accepted Answer

Question restatement: You are conducting a test of H0: μ = 12.0 versus H1: μ ≠ 12.0. After collecting data, the p-value is greater than α. Which statement best represents the conclusion?

Option analysis:
- Option: 'There is not significant evidence to suggest that μ ≠ 12.0.'
  This option aligns with the standard interpretation of a two-sided test when the p-value exceeds the significance level α. A p-value greater than α means you do not have enough evidence to reject the null hypothesis H0: μ = 12.0 at the chosen α level. In plain terms, the data are not sufficiently inconsistent with μ = 12.0 to conclude a departure from 12.0.

Why this is not interpreted as evidence that μ actually equals 12.0 with certainty: the p-value is a measure of evidence against H0, not a proof of it. A p-value > α does not confirm H0; it simply indicates that the observed data could plausibly occur under H0, given the chosen level of risk for a Type I error. There is always some probability of a Type II error (failing to detect a true effect) that is not eliminated by this result.

Why this option is consistent with standard decision rules:
- In hypothesis testing, if p-value ≤ α, we reject H0; if p-value > α, we fail to reject H0. Since p-value > α in this scenario, the appropriate concluding statement is that there is not significant evidence to conclude μ ≠ 12.0, which matches the option provided.

Potential misconceptions to avoid:
- A common error is to claim that we have proven μ = 12.0. This is incorrect because failure to reject H0 does not prove equality; it merely indicates insufficient evidence against H0 at the specified α.
- Another misinterpretation would be to state that the effect is definitively zero. The data may be compatible with many μ values near 12.0; the test simply did not provide enough evidence to declare a difference at the chosen α.

In summary, given that the p-value exceeds α, the correct interpretive statement is that there is not significant evidence to suggest that μ ≠ 12.0, which is exactly what the option asserts.

stat_400_120258_253926 PA12-2

Suppose you are conducting a test of 𝐻 0 : 𝜇 = 12.0 versus 𝐻 1 : 𝜇 ≠ 12.0 . After collecting and summarizing sample data, you find that p-value > 𝛼 . Which of the following statements represents the correct concluding statement?

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