I hope I've posted in the correct forum, because this seems not like the high school statistics I learned.
I've got two questions:
I have a set of data. The population size is 263000. The mean score is 7.578, the standard deviation is 1.274.
A subset of the data has a particular characteristic that I want to determine if it is a contributing factor in the results.
The sample (subset) size is ~60000 with a mean of 8.348 and a standard deviation of 1.175.
What is the probability, statitical significance etc, that the sample could have a mean so different from the population? In other words, is it a contributing factor in results? I'm not certain what I'm looking for or how to calculate it. I've done Z-scores at uni a long time ago, but a friend started talking about t scores and just lost me. Central Limit Theorem rings a bell somewhere, but I'm not sure what to do.
The second question is similar to the above question, but relating to proportions.
Within the population, 0.051 "failed", within the sample 0.012 "failed". What is the probability, statistical significance etc, that this could occur by random change? In other words, does this characteristic seem to have a very strong influence on results?