Need someone to check my work on finding the value of alpha in from Student t distribution? Please look at the image for more information. 
I need help with question (c), which is finding the value of alpha.
The following is given to us: $\text{mean } = 34.6, n = 47, \text{df } = 46, s(\text{SD}) = 4.093.$
The $t$ value used for the question (a) is $2.013$.
My steps are the following:
$$\text{mean $-$ (margin of  error) $= 32.80604$}$$
$$\text{(margin of error) = mean $- 32.80604$}$$
$$t\frac{s}{\sqrt b} = 1.79396$$
$$t=\frac{1.79396}{\frac{4.093}{\sqrt 47}}$$
$$t = 3.00483$$
Now I need to find alpha, but I have no idea how to use the t table to find my answer.
  Here's a link for a good $t$ table.

Looking at t-test there can be a general estimation way of calculating this as degrees of freedom being 46 is not located in table. There is an exact way to calculate but this is long winded!
Using the t table and testing at 5% sig level for 45 degrees of freedom gives a value of 1.679 since this is smaller than 3.00483 you reject the null hypothesis at the 5% level. you can also reject it at 1% level as this gives a value of 2.412 which is again smaller. Therefore you retain the alternative hypothesis! 
therefore his alpha would be 0.01 as one tailed test
Hope this helps!
