If I'm running a simple 1-sample t-test, and I have p-hat, s, n, and p, where p-hat and s come from the following type of numbers:

0
0
0
0
0
0
0
0
0
.8
.8
.8
.8
1.2
1.2
1.2
1.6
1.6
1.6
2
2
2
2
2

I.e, from only 5 different possible "scores" on a "test", can I proceed as usual with the t-test? Is there a different procedure for data like these?