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.

Question

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 restatement:
- We are looking at a one-sample t test with a fixed alpha of 0.05. Under the given hypotheses, the estimated power is stated as 0.547. Additionally, it is claimed that the minimal sample size required to reach the desired acceptable power (while keeping all other conditions the same) is 43. The answer field lists two selections: 0.547 and 43.

Analysis of option 0.547:
- This value represents the power of the one-sample t test under the specified conditions. Power is the probability of correctly rejecting the null hypothesis when a true effect exists. A power of 0.547 means there is a 54.7% chance of detecting the effect, which is below the common target power levels like 0.80. In practical terms, this indicates the study is underpowered and may frequently miss a true effect. The interpretation hinges on the effect size, sample size, and variability; with the same setup, this power value is consistent with a relatively small effect size or high variability.

Analysis of option 43 (the suggested minimal sample size):
- The claim that n = 43 is the minimal size needed to achieve the desired acceptable power implies that, given the same effect size and variance, increasing from the current sample size to 43 would raise power to the target level (often 0.80 or another predefined threshold). Whether 43 is truly minimal depends on the exact power curve for the test, which is a function of effect size, variance, and alpha. If 43 is asserted as the minimal n, it would mean that any smaller n would yield power below the target, while 43 just meets or slightly exceeds the target. This reasoning is consistent with standard power analysis logic: larger samples yield higher power, and a particular cutoff (the desired power) defines a corresponding required n.

Why the choices align with common concepts:
- Power, alpha, effect size, and sample size are interdependent in a one-sample t test. A power of 0.547 at alpha 0.05 is a typical sign of insufficient power for many practical studies, especially if the goal is 0.80. Increasing the sample size from the current value to 43 is a plausible route to push power up to the acceptable level, assuming the effect size remains the same and variance does not change unfavorably.

Possible misconceptions to avoid:
- It would be incorrect to interpret 0.547 as an adequate power level for most research standards; the common benchmark is around 0.80 or higher. If someone claimed 0.547 is the target power, they might be misunderstanding the typical goals of power analysis.
- Assuming any specific target power (like 0.95) without stated justification can lead to wrong conclusions about the required sample size; the minimal n depends on the chosen target power.
- Declaring 43 as minimal without examining the exact power curve and effect size could be misleading; small changes in those parameters can shift the required n.

In summary: the 0.547 figure reflects the current, underpowered state of the test under the given conditions, while 43 is presented as the smallest sample size that attains the desired power level if all other factors stay the same. The two selections correspond to the stated statements about the test’s power and the recommended sample size under the specified 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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