Speech analysis could provide an indicator of cognitive health and help develop clinical tools for automatically detecting and monitoring cognitive health progression. The Mini Mental Status Examination (MMSE) is the most widely used screening tool for cognitive health. But the manual operation of MMSE restricts its screening within primary care facilities. An automatic screening tool has the potential to remedy this situation. This study aims to assess the association between acoustic features of spontaneous speech and assess whether acoustic features can be used to automatically predict MMSE score. We assessed the effectiveness of paralinguistic feature set for MMSE score prediction on a balanced sample of DementiaBank's Pitt spontaneous speech dataset, with patients matched by gender and age. Linear regression analysis shows that fusion of acoustic features, age, sex and years of education provides better results (mean absolute error, MAE = 4.97, and R2 = 0.261) than acoustic features alone (MAE = 5.66 and R2 =0.125) and age, gender and education level alone (MAE of 5.36 and R2 =0.17). This suggests that the acoustic features of spontaneous speech are an important part of an automatic screening tool for cognitive impairment detection.Clinical relevance- We hereby present a method for automatic screening of cognitive health. It is based on acoustic information of speech, a ubiquitous source of data, therefore being cost-efficient, non-invasive and with little infrastructure required.