You have to tell us more about your sampling frame. The previous  replies assume a simple random sampling frame. It means that each fisherman should have the same probability to be sampled. This is rarely the case, because you'd need a full list of your 7,000 fishermen... Instead, people often sample villages first, and then fishermen within villages (2-degree sampling). Moreover, it is better to stratify the population according to the injury risk. For example, the risk might depend on the fishing method, or boat size, etc. A stratified sample provides more accurate estimates, i.e. you can reach the same precision with a smaller sample size (with respect to a simple random sampling frame).

Dewenati !!!

But with which sampling frame???

I would suggest you see Scheaffer, Mendenhall and Ott, Elementary Survey Sampling where all of these designs are discussed and example calculations are given. BTW, unless I missed it somewhere, you also need a bound on the error of estimation. Best Wishes.

Samba -

First, sample sizes are based on a standard error goal, which is often expressed in a confidence interval, or it could be on power to go with your 'significance' level.  A p-value is driven by sample size, so it is easier to get a small one, if your sample size is large, regardless as to effect size.  You have to be careful of what this means.

 https://www.researchgate.net/publication/262971440_Practical_Interpretation_of_Hypothesis_Tests_-_letter_to_the_editor_-_TAS

You need to consider "effect size." 

I suggest not using hypothesis tests.

The sample size 'formulas' you likely see on the internet are for sampling for proportions from an infinite population, with simple random sampling, and for the worst case, where p=q=0.5. This may not be of use to you.  For each variable/question you will need to use (1) a method compatible with that type of data - often continuous or perhaps yes/no, (2) what sample design is best - stratification often lowering sample size needs, whereas clustering may be substantially more convenient, (3) and very importantly, the standard deviation of the population (or in each stratum).  Number 3 may require a pilot study. 

Also, because you are investigating a finite population, you may need a finite population correction (fpc) factor. (I have a definition on my RG page that I did for a Sage Pub encyclopedia.)

There are chapters on sample size in the following two survey sampling textbooks, and more information in many others you could find:

Cochran, W.G(1977), Sampling Techniques, 3rd ed., John Wiley & Sons  

and  

Blair, E. and Blair, J(2015), Applied Survey Sampling, Sage Publications.

In Cochran, he explains sample size in a chapter for simple random sampling, and in succeeding chapters, he relates information on other designs and the impacts.

Unless you are sampling for proportions and have a small sample compared to the population size, for simple random sampling, and the proportion is expected to be near 0.5, there isn't a one-size-fits-all formula solution.  It can get complicated. You may need a pilot study to judge this, as well as test a questionnaire, logistics, and/or whatever considerations you might have.

Note that if you want to look at various levels of experience, you might stratify, but that isn't exactly stratification because you really want to know information for each group, not just get better overall (aggregate) estimates. You would effectively be comparing two or more populations.  You need a good estimate as to how many are in each of those subpopulations.  And/or you might do regressions of variables of interest versus age, but age isn't quite a continuous variable, and things could get messy.  So unless you are happy to compare a few age groups, this may be very involved.  (I have done a lot with continuous data regressions, but am not familiar with the other kinds.)  If you look at a number of age-group subpopulations and investigate each, you may need to consider the fpc in each group, just as in stratification.

I urge you to decide ahead of time exactly what you will do with the data, and what design(s) you are using, considering every variable of importance to you.  People sometimes may gather data and then wonder what to do with it.  You need to plan first.  Asking about your sample size needs was a good step. 

Cheers - Jim

Article Practical Interpretation of Hypothesis Tests - letter to the...

You need to do a power calculation to determine the sample size you need.

For a straightforward Pearson's correlation coefficient here is a calculator to allow you to do that.

http://www.sample-size.net/correlation-sample-size/

Leave alpha at 0.05 and beta at 0.2 (so that power is set at 80%). If you want greater power eg 90%, then set beta to 0.1.

Put in the value for r ie what you expect the correlation coefficient to be or what correlation you consider to be important enough to your study. For example you might decide that a correlation coefficient of 0.7 or above is important enough to detect and show that it is significant. So you will then choose r=0.7 in the calculator.

You will get out the sample size that you will need to ensure you have enough power to detect the correlation that you think is important enough to detect. Having detected that correlation then the sample size should then be large enough to show your correlation coefficient is significant and so you will need to test it for significance.

In this way you could look at the correlation between number of years fishing (ie experience) and injuries. However watch out for confounders as number of years fishing may increase with age and it is age which might be the important factor not amount of fishing experience, so you might want to stratify in age groups, or you might want to do multiple regression in which case you will need a different power formula to determine sample size. Sometimes power formulae do not exist for complicated studies and then you need monte carlo methods.

see

http://hbanaszak.mjr.uw.edu.pl/TempTxt/FinalSEMsingle.pdf

Here is information on power calculations for other simpler tests.

https://faculty.washington.edu/jelmore/articles_online/Wittes-Sample_size_calc.pdf

About 364 using Sample Size Calculator app created by Stats Assistance.