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

View Explanation

Log in for full answers

Similar Questions

Which one is true?

For an upper-tail hypotheses about a population mean with σ known and α=5%, which one is the rejection region?

For a given sample, the P-value for upper tail test is x, and the P-value for two-tailed test is y, then

For a two-tailed hypothesis test with a test statistic value of z = 2.09, the p-value is _____.

For a sample size of 30, changing from using the t distribution to using the standard normal distribution in a hypothesis test _____.

Exhibit 9-5 n = 16 H0: μ ≥ 80 = 75.607 Ha: μ < 80 σ = 8.6 Assume the population is normally distributed. Refer to Exhibit 9-5. The p-value is equal to _____.

Exhibit 9-1 Refer to Exhibit 9-1. If the test is done at a .01 level of significance, the null hypothesis should _____.

Which of the following statements descrbes best the characteristics of the one-tailed and two-tailed tests in statistical hypothesis testing?

More Practical Tools for International Students

Exam Browser Assistant

Stylized Writing Assistant

Plagiarism Checker Assistant

Citation Assistant

In-Class Translation Assistant

Class Notes Assistant

Quiz Search Assistant

Past Exam Questions by School

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler