This study explores the connection between social media, specifically Twitter, and the stock market, aiming to illustrate if social media sentiments can predict short-term stock market trends. Our study critically examines the predictive power of social media sentiments, emphasizing the need for a thorough exploration, especially during periods of high social media activity. We suggest considering the orientation of public emotion, known as the intensity of public sentiments, as a crucial factor in understanding the impact of social media on stock prices. Our research methodology used advanced sentiment analysis tools like TextBlob and VADER. We use Z-scores to apply for data standardization, and we take advantage of predictive models such as Linear Regression, Random Forest Regressor, and Gradient Boosting Regressor. We choose Apple's tweets and corresponding stock prices as a test dataset to check predictive models. Also, we use Mean Squared Error (MSE) as a crucial metric to evaluate model performance. Through analyzing results, we find out that noticeably lower MSE for the Random Forest model substantiates its accuracy in predicting stock prices within this dataset. These results demonstrate the Random Forest model's empirical effectiveness in predicting stock values based on sentiment in tweets, hence confirming its suitability for short-term forecasting. In summary, our study explains the possibility of using social media sentiments, particularly on Twitter, as predictive indicators for short-term stock market trends.