I am doing a two sample hypothesis problem that goes like this:
Research has shown that good hip range of motion and strength in throwing athletes results in improved performance and decreased body stress. The article “Functional Hip Characteristics of Baseball Pitchers and Position Players” (Am. J. Sport. Med., 2010: 383–388) reported on a study involving samples of 40 professional pitchers and 40 professional position players. For the pitchers, the sample mean trail leg total arc of motion (degrees) was 75.6 with a sample standard deviation of 5.9, whereas the sample mean and sample standard deviation for position players were 79.6 and 7.6, respectively. Assuming normality, test appropriate hypotheses to decide whether true average range of motion for the pitchers is less than that for the position players (as hypothesized by the investigators).
Using the information from the question I was able to get a t value of $-2.63$, from what I understand from here I'm supposed to compare this -2.63 to a critical value I get from the t table, or I can get find the p-value (I got $0.0043$ from the normal table) and compare it to alpha which is the significance level. For both of these I don't really understand on which situations I'm supposed to be using for which method, It would be great if someone could explain this to me too. But regardless the main issue I have is that both of these requires a significance level to figure out, which wasn't given to me. Since I didn't know how to proceed I went to look at the answer to this question, which said this:
Because the one-tailed P-value is $.005 < .01$, conclude at the $.01$ level that the difference is as stated.
The alternative hypothesis was chosen because the P value was lower than the significance level of $.01$ but if they had just chosen a smaller significance level(e.g. $0.001$), then the alternative hypothesis would have been rejected
So here my question is how did they know that a significance level of $.01$ was the level they are supposed to compare to? Did they just choose it because there was no significance level given in the question?