We study a model where a data collector obtains data from users through a payment mechanism, aiming to learn the underlying state from the elicited data. The private signal of each user represents her knowledge about the state; and through social interactions each user can also learn noisy versions of her social friends' signals, which is called `learned group signals'. Thanks to social learning, users have richer information about the state beyond their private signals. Based on both her private signal and learned group signals, each user makes strategic decisions to report a privacy-preserved version of her data to the data collector. We develop a Bayesian game theoretic framework to study the impact of social learning on users' data reporting strategies and devise the payment mechanism for the data collector accordingly. Our findings reveal that, in general, the desired data reporting strategy at the Bayesian-Nash equilibrium can be in the form of either a symmetric randomized response (SR) strategy or an informative non-disclosive (ND) strategy. Specifically, a generalized majority voting rule is applied by each user to her noisy group signals to determine which strategy to follow. Further, when a user plays the ND strategy, she reports privacy-preserving data completely based on her group signals, independent of her private signal, which indicates that her privacy cost is zero. We emphasize that the reported data when a user plays the ND strategy is still informative about the underlying state because it is based on her learned group signals. As a result, both the data collector and the users can benefit from social learning which drives down the privacy costs and helps to improve the state estimation at a given payment budget. We further derive bounds on the minimum total payment required to achieve a given level of state estimation accuracy.