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

Question

BlackTom AI · Accepted Answer

We start by identifying what x and y represent in hypothesis testing terms. Option 1: None of the other three. This would be true only if the relationship between x and y did not follow the usual one-tailed vs two-tailed relationship, which is not the case in standard tail probability properties, so this option is unlikely. Option 2: x = y. In a typical z or t test with a single observed statistic, the two-tailed p-value y is generally larger than the upper-tail p-value x, because y accounts for deviation in both directions, effectively doubling the evidence against the null compared to the one-sided test for the same magnitude of statistic. Equality would require a degenerate scenario or a boundary condition, not the common case. Option 3: x < y. For a standard upper-tail p-value x = P(Z > z) and the two-tailed p-value y = P(|Z| > |z|) which equals 2*P(Z > |z|) when |z| is used, we typically have y = 2x for a positive z, or at least y > x in general; hence the two-tailed p-value is larger than the one-sided p-value for the same observed statistic. This makes x < y the correct and expected relationship. Option 4: The relative size of x and y depends on α. The definition of p-values is independent of the chosen significance level α; α affects the decision rule (reject or not) but not the numerical relationship between the one-sided and two-sided p-values themselves. Therefore this statement is incorrect. Thus, among the provided choices, the one that aligns with the standard relation between one-tailed and two-tailed p-values is that x is less than y.

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

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