Question: The sign test can be extended to a test of hypotheses about an arbitrary quantile of a distribution rather than just the median. Let p

The sign test can be extended to a test of hypotheses about an arbitrary quantile of a distribution rather than just the median. Let θp be the p quantile of a distribution, and suppose that X1, . . . , Xn form an i.i.d. sample from this distribution.
a. Let b be an arbitrary number. Explain how to construct a version of the sign test for the hypotheses
H0: θp = b,
H1: θp ≠ b,
at level of significance α0. (Construct an equal-tailed test if you wish.)
b. Show how to use this version of the sign test to form a coefficient 1− α0 confidence interval for θp.

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