For specific values such as 1.6449 I can simply use a table to know that the significance level is 5%. How do I figure this out with values that aren't as common?
EDIT: Information that I initially left out,
Null Hypothesis: mean=3.55
Alternate Hypothesis: mean<3.55
n=49
Standard Deviation = 6.2
Eventually I get to P(X≤1.73)=α, and using the table I get a z value of 0.9582.
(With X being the critical value)
On
Using the data sheet given here: OCR List of Formulae (page 19), we can read off that a z-value of 2.05 gives a p-value of 0.9798, and as shown by the extra columns to the right, if we wish to find a p-value for $z=2.054$, then add 2 onto the 4th decimal place of the previous result, which gives $p=0.9800$. So the significance level of such a test would be $2\%$.
You need a more detailed table... or since it's the year 2000 use a software package that has the normal cumulative in it.
For instance I open an octave prompt and type: "normcdf(-2.0537)" and it gives me "0.020002".. looks like it's about 2%. R or Excel or pretty much any data analysis package will have the function implemented.
Wolfram alpha is a bit difficult for getting the normal cumulative function for whatever reason, but I was able to get it to work: https://www.wolframalpha.com/input/?i=standard+normal+cdf+(-2.0537)