Question

6. The median, or Q2, is nothing special. When creating a sign test, we could have designed the testing infrastructure around the first quartile, Q1, instead. Suppose we set a null hypothesis of Ho: q = go, where q is a symbol for the first quartile, go is a constant, and we are dealing with a continuous random variable X. a. Assuming Ho, we collect n values from X: Xi,..., Xn If U is the number of observations less than go, give the exact distribution of U. b. For large n, U will be approximately normal. Using this fact, design a test statistic that could be used for large sample testing

Answer 1

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