The goal of this research brief, and of the longitudinal survey that informs it, is to address the question of gov- ernment legitimacy in China using the most objective and quantitative methods currently available. Our sur- vey1 contains data from eight separate waves between 2003 and 2016, and records face-to-face interview responses from more than 31,000 individuals in both urban and rural settings. As such, it represents the lon- gest-running independent effort to track citizen ap- proval with all four levels of the Chinese government across time (ranging from the township, to the county, to the provincial, and finally to the central government).

The sample size was over 10 times what you claimed, and it was absolutely statistically relevant. Here’s a neat link on sample sizes, 31,000 is more than plenty. There indeed were discrepancies between the urban and rural, that’s because historically rural areas have been slower to develop than urban areas, and now rural areas are made a priority to close the gap.