Null and alternate hypothesis

#1
Hi-
I have a problem that begins, "Suppose you wish to test the null hypthesis that u=50 vs the alternate hypothesis that u<50...."and then it goes on to ask that i compute some infomation, but my problem is, i thought the null and alternate had to be the same signs, for example Null = 50, so Alternate =50, not one is equal to and the other less than...does this mean the distribution would be one tailed instead of 2? Once more, i thought if it were one tailed it would read u>50 (null) and u<50 (alternate)....does this make sense to anyone???
Thanks!=)
 
#2
Hi-
I have a problem that begins, "Suppose you wish to test the null hypthesis that u=50 vs the alternate hypothesis that u<50...."and then it goes on to ask that i compute some infomation, but my problem is, i thought the null and alternate had to be the same signs, for example Null = 50, so Alternate =50, not one is equal to and the other less than...does this mean the distribution would be one tailed instead of 2? Once more, i thought if it were one tailed it would read u>50 (null) and u<50 (alternate)....does this make sense to anyone???
Thanks!=)
Yes, it does. It is a left-tailed, one-tailed test. Your notation is correct.