(In some of the exercises that follow, we must make assumptions such as the existence of normal distributions with equal variances.) Let X and Y denote the tarsus lengths of male and female grackles, respectively. Assume that X is N(Ux. o'x)and Y is N(UY. 'y ). Given that n = 25, x = 33.80,5 x= 4.88, m = 29, y = 31.66, and s'= 5.81, test the null hypothesis Ho: Ux = Py against H1: Ux > My with a = 0.01. (In some of the exercises that follow, we must make assumptions such as the existence of normal distributions with equal variances.) When a stream is turbid, it is not completely clear due to suspended solids in the water. The higher the turbidity, the less clear is the water. A stream was studied on 26 days, half during dry weather (say, observations of X) and the other half immediately after a significant rainfall (say, observations of Y). Assume that the distributions of X and Y are Mux, 62) and MuY, 02). respectively. The following turbidities were recorded in units of NTUs (nephelometric turbidity units): x: 2.9 14.9 1.0 12.6 9.4 7.6 3.6 3.1 2.7 4.8 3.4 7.1 7.2 y: 7.8 4.2 2.4 12.9 17.3 10.4 5.9 4.9 5.1 8.4 10.8 23.4 9.7 (a) Test the null hypothesis Ho: Ux = My against H1: Ux