Question 1: With the appropriate hypotheses, when completing a one-sample t test, at α = 0.05, the estimated power is 0.547 . You would minimally need a sample size of 43 to achieve the desired acceptable power, when keeping all other conditions the same.

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Question 1:  With the appropriate hypotheses, when completing a one-sample t test, at α = 0.05, the estimated power is 0.547 . You would minimally need a sample size of 43 to achieve the desired acceptable power, when keeping all other conditions the same.

BlackTom AI · Accepted Answer

Let’s unpack what the statement is presenting and then evaluate each piece.
Option 1: '0.547' as the estimated power at α = 0.05 for the one-sample t test under the given hypotheses.
- Power is the probability of correctly rejecting the null hypothesis when the alternative is true. An estimated power of 0.547 means there is about a 54.7% chance of detecting the effect under the specified conditions. This is a plausible figure for a study with a modest effect size and sample size, and it aligns with the reported scenario that the power is below conventional targets like 0.80. Since the question states that this is the estimated power under the given hypotheses, this value is consistent with the setup and is therefore correct as the reported power.

Option 2: '43' as the minimal sample size needed to achieve the desired acceptable power while keeping all other conditions the same.
- Sample size directly influences power: increasing n increases the test’s ability to detect an effect. If the current power is 0.547 and the problem states that a sample size of 43 is the minimum required to reach the acceptable (target) power, then 43 would be the threshold at which power meets or exceeds the target. This reflects a common planning step in power analysis: identify the n needed to reach the pre-specified power level (e.g., 0.80). Assuming the problem’s wording uses 'minimal' appropriately and all other factors (variance, effect size, alpha) are held constant, selecting n = 43 as the minimum to reach the target power is logically consistent.

Why these interpretations make sense together:
- The current estimated power (0.547) is a function of the present sample size and the assumed effect size under the alternative. The statement about needing n = 43 to achieve the target power implies that at n = 43, the power would meet or exceed that target, whereas smaller n would yield power below the target. This creates a coherent narrative: modest power at the current n, and a specific, larger n needed to reach acceptable power levels.

In summary, both options reflect typical components of a power analysis for a one-sample t test under predefined hypotheses and α = 0.05: the power estimate given for the current design and the sample size requirement to reach the desired power target. If either statement were false, it would imply a mismatch between the reported power and the sample size needed to attain the target, which would contradict the problem’s setup.

STAT 460, Section 001: Inter Appl Stat (22511--UP---P-STAT----460-------001-) Lab Quiz 9: Stat 460

Question 1: With the appropriate hypotheses, when completing a one-sample t test, at α = 0.05, the estimated power is 0.547 . You would minimally need a sample size of 43 to achieve the desired acceptable power, when keeping all other conditions the same.

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