Providing provenance in scientific workflows is essential for reproducibility and auditability purposes. Workflow systems model and record provenance describing the steps performed to obtain the final results of a computation. In this work, we propose a framework that verifies the correctness of the statistical test results that are conducted by a researcher while protecting individuals' privacy in the researcher's dataset. The researcher publishes the workflow of the conducted study, its output, and associated metadata. They keep the research dataset private while providing, as part of the metadata, a partial noisy dataset (that achieves local differential privacy). To check the correctness of the workflow output, a verifier makes use of the workflow, its metadata, and results of another statistical study (using publicly available datasets) to distinguish between correct statistics and incorrect ones. We use case the proposed framework in the genome-wide association studies (GWAS), in which the goal is to identify highly associated point mutations (variants) with a given phenotype. For evaluation, we use real genomic data and show that the correctness of the workflow output can be verified with high accuracy even when the aggregate statistics of a small number of variants are provided. We also quantify the privacy leakage due to the provided workflow and its associated metadata in the GWAS use-case and show that the additional privacy risk due to the provided metadata does not increase the existing privacy risk due to sharing of the research results. Thus, our results show that the workflow output (i.e., research results) can be verified with high confidence in a privacy-preserving way. We believe that this work will be a valuable step towards providing provenance in a privacy-preserving way while providing guarantees to the users about the correctness of the results.