population and subsamples : mean equality?

I want to perform a two sample test, to see whether theirs means are equals. One of the sample is rather big (#60000 values) and represents the scores of a whole population. This population is partitioned in small classes of less that 1000 people. The other sample of the test is a subsamble of the former. It corresponds to people of the same class. So, each time, there is less than 1000 values in it. I have no idea about the variances, so I'd think of using Welch's t-test.

But I'm concerned regarding the independence hypothesis: can it be valid, considering that the second sample is negligible when compared to the overall population?

• There are two ideas. First, the test is going be a one-sample test since you compare smaller groups' mean to a population (supposed) mean. Second, why would you want to do this given that hypothesis check on a sample statistic is about where the sample is from the specified distribution? Commented Oct 27, 2017 at 16:45
• from the specified distribution. Sorry, from specified population. Which you already know as being true. Commented Oct 27, 2017 at 17:02
• Could you please clarify the means of what you want to compare? Commented Oct 27, 2017 at 17:40
• I do this because I want to reject null hypothesis H_0 is {means are equal} For example : To see whether a class of 500 people that have the same job or the same education (i.e. a subsample of the whole population), do have a mean score different from the average. Commented Oct 27, 2017 at 17:55
• So you want to compare to total population average, do you? Ah, given that subsamples are not randomly drawn, I see now that you ondeed can see significant differences. Commented Oct 27, 2017 at 18:15