Suppose the null hypothesis is p = 0.5 and we fail to reject H0. Under this scenario, 0.5 is a reasonable value for the true population proportion.

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In this true/false question, we start by restating the claim to be evaluated: 'Suppose the null hypothesis is p = 0.5 and we fail to reject H0. Under this scenario, 0.5 is a reasonable value for the true population proportion.'
Option 1: True. The intuition here is that when we fail to reject the null hypothesis, the data provided do not provide strong evidence against p = 0.5. Consequently, p = 0.5 is a plausible value for the true proportion consistent with the observed data, given the test's sampling variability. This alignment with the null value is expected because the test was not able to demonstrate a deviation from 0.5. However, this is not a guarantee that p is exactly 0.5; it merely indicates that 0.5 is not contradicted by the data at the chosen significance level. The key nuance is that plausibility does not equal proof, and the conclusion depends on power, sample size, and variability.
Option 2: False. If you interpret 'reasonable value' as meaning 'the true proportion must be 0.5,' then failing to reject H0 does not establish that. A failure to reject can occur due to insufficient power, small sample size, or high variability, even when the true p is different from 0.5. In other words, 0.5 being consistent with the data does not force the true value to be exactly 0.5; the true proportion might be near 0.5 or could be somewhat different but not detected given the study design.
Additional nuance: The decision to reject or fail to reject is about evidence against the null at a specified alpha level. Absence of rejection is not the same as affirmative evidence that the null is true or that 0.5 is the precise truth. Therefore, while 0.5 can be regarded as a reasonable value to consider, especially as the null hypothesis, one must acknowledge the possibility that the true proportion differs and that the study may lack the power to detect that difference.
In summary, the reasoning hinges on distinguishing 'plausible given the data' from 'provably true,' and acknowledging that non-rejection does not guarantee p = 0.5, though it makes 0.5 a reasonable candidate value to consider with the given data.

FA25_QTM_100_3 5.30: True or false.

Suppose the null hypothesis is p = 0.5 and we fail to reject H0. Under this scenario, 0.5 is a reasonable value for the true population proportion.

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FA25_QTM_100_3 5.30: True or false.

Suppose the null hypothesis is p = 0.5 and we fail to reject H0. Under this scenario, 0.5 is a reasonable value for the true population proportion.

View Explanation

Log in for full answers

Similar Questions

Which one is true?

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

More Practical Tools for International Students

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