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Suppose you have $H_0: \theta = 1, H_a: \theta > 1$. Is the limit($\theta > \infty$)P-value > expected value of P-value under null hypothesis?

Attempt: No, the p -value is smaller under $H_a$ so the inequality above should be reversed.

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This question is barely comprehensible. Please proofread it and try to use more standard terminology as far as possible. For instance, $\theta > \infty$ makes no sense -- do you mean $\theta\to\infty$? You can get that symbol using the command \to. By "under null", do you mean "less than zero"? – joriki Nov 14 '11 at 20:55
Under null hypothesis is statistical jargon for assuming that $H_0$ holds. – Did Nov 14 '11 at 21:11
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Normally one sees the definite article: "under the null hypothesis". Joriki, you are right that the language of the question is opaque. But the phrase "under the null hypothesis" is standard and seen daily. – Michael Hardy Nov 15 '11 at 4:46

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