Power of a Ten-Flip Test
A coin is flipped 10 times. To test $H_0:p=1/2$ against $H_1:p>1/2$, reject $H_0$ when 8 or more heads are observed. If the coin's true probability of heads is $p=3/4$, what is the power of this test? Give a decimal rounded to three places, or the exact fraction.
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Source: Original problem written for AxiomIQ.