Independent normal random variables X and Y have means μ and pu respectively, and both have variance 1. The ratio p of their means is of particular interest. Show that the distribution of YpX depends upon p, but not upon μ. A single observation is made on each of X and Y, resulting in values x and y respectively. Use your result to test the hypothesis p = 1 against an alternative p # 1 at the 5% level when (i) x = 0.3 and y = 2.7, (ii) x = 0.3 and y = 1.5.

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