What does the phrase "scientific studies of statistically significant samples of people" mean exactly?

One of Smith's observations was that:

"the condition of the labouring poor, of the great body of the people, seems to be the happiest and the most comfortable".

Adam Smith: An Inquiry into the Nature and Causes of the Wealth of Nations, Chapter 8

From the limited context of your question, it seems likely that Conlin is inviting his reader to consider some hypothesis in the light of Smith's view, and to contrast this negative correlation of happiness with income (poor group = happy; rich group = less happy) with the positive correlation that applies to individuals at any instant (the richer you are the happier you feel). It is this mismatch of correlations that lies at the heart of Richard Easterlin's paradox

Wikipedia: Easterlin Paradox

From this standpoint, Conlin's sentence is essentially about these two opposing views of measured correlations between perceived happiness and income. How happiness and income are measured is doubtless important and subject to controversy, but the measurements themselves are (at least in principle) amenable to statistical analysis. Hence Conlin advises his readers to keep in mind that statistical techniques are available and should be used to inform any analysis of happiness-income data and any conclusions about them.

Details of sampling statistics are not given in the sentence but are not crucial to your question or its answer.