The power of supercomputers derives from the idea of parallel processing. Engineers at Cray Research ...

The power of supercomputers derives from the idea of parallel processing. Engineers at Cray Research are interested in determining whether one of two parallel processing designs produces faster average computing times, or whether the two designs are equally fast. The following are times in seconds of independent random computations using the two designs. Design I 2.1 2.2 1.9 2.0 1.8 2.4 2.0 1.7 2.3 2.8 1.9 3.0 2.5 1.8 2.2
Design II 2.6 2.5 2.0 2.1 2.6 3.0 2.3 2.0 2.4 2.8 3.1 2.7 2.6
 

Assume the two populations are normal and the population variances are equal. Is there evidence at the 0.05 level that one of the two processes is faster than the other?
 

What are its Type I error and Type II errors?