The conventional Z-test for correlation, grounded in classical statistics, is typically employed in situations devoid of vague information. However, real-world data often comes with inherent uncertainty, necessitating an adaptation of the Z-test using neutrosophic statistics. This paper introduces a modified Z-test for correlation designed to explore correlations in the presence of imprecise data. We will present the simulation to check the effect of the measure of indeterminacy on the evolution of type-I error and the power of the test. The application of this modification is illustrated through an examination of heartbeat and temperature data. Upon analyzing the heartbeat and temperature data, it is determined that, in the face of indeterminacy, the correlation between heartbeat and temperature emerges as significant. This highlights the importance of accounting for imprecise data when investigating relationships between variables.