1. [10 marks) There are two samples with sizes 111 and 11.3 from two populations with means #1, a? and varianCes a? and 0%, resPectively. We want to test whether p1 2 p2 or not. For each of the follmwing caSes, decide what test statistic should he uSed and then write the test statistic clearly. (a) [2 marks} two samples with sizes 111 2 30, n2 2 3'0. and 1mm of and 0%. {b} (2 marks} two samples with sizes 711 2 30, 11.2 :3 30, and unknown or? and erg. ( {e} 2 marks} two samples with sizes at least one of in and 112 strictly smaller than 30, and known a? and (IE, and from independent and normally distributed populations. (d) (2 marks} two samples with sizes at least one of 111 and n2 strietlf,r smaller than 30, and un- known oil2 and 0%, but a? = 0%, and Erom independent and normally distributed populations. (e) (2 marks} two samples with sizes at least one of 111 and a; strictly smaller than 30, and un- known cr? and 0%, and 0'? 9E avg, and from independent and normally distributed populations