Conceptual ideas about Hypothesis testing and distributions

I've read the stickied thread about this topic, but I still have some questions/I want to confirm that I'm doing this correctly.

We have experimental data that maps golf shots to how far away they are from the hole being aimed at. The data has the location of the hole labeled at 0, values shorter than the hole labeled at values from -5 to -1 and values farther than the hole labeled at values from 1 to 5.

So the problem is as follows:

Use the t-distribution to determine if you would reject or fail to reject the null hypothesis (that you shoot the proper distance to the whole). Use a significance value of .01. Then calculate a P-value

So I can calculate the sample standard deviation of the distance along with the sample mean. THen since the null hypothesis is that we hit the hole (origin), $\displaystyle \mu_0 $ would be 0 and $\displaystyle Ha : \mu_\alpha \neq 0$

So for my test statistic it would be :

$\displaystyle t_{\text{calc}} = \frac{\text{sample mean dist}-0}{\frac{\test{sample deviation of distance}}{\sqrt{\text{num tests}}}} $

In my case, sample standard deviation was 5.7 and number of tests was 30. The sample mean was .1, so in all I get:

$\displaystyle \frac{.1}{\frac{5.7}{5.47722558}} = \frac{.1}{1.04067286} = .0961$

t using .1 (rounded up) and N-1 = 29 gives 1.311

And t using a/2 = .1/2 = .05 and 29 gives 1.699

So since using the significance is less than the value I calculated, I should reject the null, correct? Or should the first equation be a lookup with .961/2 = .481. In the latter case I don't have a table entry for .481, but rounding to .5 would make the point of this calculation moot, so I'm guessing that since the value of the t distribution increases as alpha decreases, my calculated value is >= the value using the significance, so I shouldn't reject H0?

As for the P value, since this is a two-tailed test, I could use $\displaystyle 2 * (1- {\phi}_{.5 ,29})$?

Thanks.