Could any one please confirm the following;

I have two columns of data (temperature) that I would like to compare. I would like to understand the statistical relationship between the two. I have about 1200 temperature measurements.

Is the following approach valid?

Find the correlation coefficient: r

I then find the coefficient of determination: r2

I then find the t value to test significance of a correlation coefficient using this formula:

t = r * SQRT((n-2)/(1-r^2))

If the value of t is less than the critical value, which is found from a table corresponding to the desired significance level, then the null hypothesis cannot be rejected i.e. there is no relationship. If its greater then that level of significance is achieved.

When I use my figures I get a r value of 0.73 and so r^2 = 0.53
When I use n = 1200 it gives a t-value = 36.85
When I look up critical values for two tailed significance the 0.0001 significance level is 3.91 for n = 1000 (this was the largest value for n given).

My questions are:

Is this approach correct?

Because 36.85>>3.91 does this mean that indeed there is a very strong positive correlation and also has a very high level of significance??

Does it matter which table of critical values I use i.e. single or two-tailed critical values?

Any help would be greatly appreciated. Thanks.