# How to determine sample size if only the population size is known?

I was asked to be a statistician in a research (survey). The respondents were hospital personnel from our local hospital with a population size of 173. Respondents were asked (via questionnaire) what they think about the implementation of healthcare waste management practices in the hospital, and they may choose Fully Implemented, Partially Implemented or Not Implemented for each question. The researcher distributed the questionnaires to the whole population but she's being advised by her teacher to just use a sample size for the research. Now I do know of Slovin's formula which is widely used in our country but is now being questioned.

This is the formula

n = N/(1+Ne^2)
where:
n = sample size
N = pop size
e = margin of error


I don't think i will be using it if it is being questioned. What method would you use to determine the sample size in this case?

• Welcome to CV. Since you’re new here, you may want to take our tour, which has information for new users. Out of curiosity, do you know why the teacher gave such an advice? – T.E.G. - Reinstate Monica Oct 12 '17 at 17:06
• I don't know too. I figured 173 population size is manageable already since all of them are located in the same place, and I already have all the questionnaires filled by the respondents. But, she insist that the professor wants her to perform a stratified random sampling and of course she'll only follow him/her. – JohnStephen.19 Oct 12 '17 at 18:01
• Have there been given a reason to only use a sample when the complete population is available? Seems pretty strange. – kjetil b halvorsen Oct 12 '17 at 19:07
• Are all the questionnaires completed? No follow-up is required? – RoryT Oct 13 '17 at 0:24
• yeah, all questionnaires are completed. Anyway, I just read that formula above was from Yamane and applicable for dichotomous response only and assumes 95% confidence interval and p=0.5. How do you then get the sample size if the response is polythomous and you don't know the variance? – JohnStephen.19 Oct 13 '17 at 1:20