What conclusion for a test would correctly detect a difference between the actual parameter and the hypothesized value for the parameter?

c08.p089.q0008

Question

What conclusion for a test would correctly detect a difference between the actual parameter and the hypothesized value for the parameter?

c08.p089.q0008

BlackTom AI · Accepted Answer

Question restatement: What conclusion for a test would correctly detect a difference between the actual parameter and the hypothesized value for the parameter?

Answer options: (none provided in the data)

Analysis of what’s available:
- At present, there are no answer choices to evaluate. Without explicit options, we cannot assess which specific conclusion (from a list) would be deemed correct.

General reasoning about hypothesis testing that applies here:
- When testing a null hypothesis H0: parameter = hypothesized value, the goal is to determine whether the observed data provide enough evidence to conclude that the true parameter differs from the hypothesized value.
- The typical decision rule is: if the p-value is less than the chosen significance level alpha, or if the test statistic falls into a rejection region, then we reject H0; otherwise, we fail to reject H0.
- A two-sided alternative (parameter ≠ hypothesized value) is most common for detecting any difference from the hypothesized value. In that case, evidence could come from an extreme value of the estimate in either direction.
- If the test is one-sided (e.g., parameter > hypothesized value or parameter < hypothesized value), the rejection region only lies in one tail of the distribution. That affects the conclusion but not the core principle: substantial evidence against H0 leads to rejection.
- A correct conclusion to detect a difference is: reject H0 when the data show sufficient evidence that the true parameter is not equal to the hypothesized value, or fail to reject H0 when evidence is insufficient.

Common misconceptions to avoid:
- “Failing to reject H0” does not prove H0 is true; it means there isn’t strong enough evidence against H0 given the data and alpha level.
- “Accepting H0” is rarely appropriate in strict hypothesis testing; we typically phrase it as “do not reject H0.”
- Interpreting a non-significant result as evidence of no difference is incorrect because it could reflect low power or small sample size rather than equivalence.

In summary, once options are available, the correct choice will align with the principle that a difference is detected by rejecting H0 when the test indicates significant evidence against the hypothesized parameter value, typically via a small p-value (below alpha) or a test statistic in the rejection region. If the provided options include statements like “Reject H0” in the context of a two-sided test indicating a difference, that would generally be the correct inference; if they instead say “Fail to reject H0,” that would be incorrect for detecting a difference.

BTRY3010/BTRY5010/STSCI2200/STSCI5200 Practice Quiz For Skipped Notes - ( Pages 136, 137 )

What conclusion for a test would correctly detect a difference between the actual parameter and the hypothesized value for the parameter? c08.p089.q0008

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