This study examines the relationship between students' attitudes toward artificial intelligence (AI) and both AI competence and conceptions. 176 UK university students completed a survey where they were asked to rate statements in relation to their attitudes towards AI, their AI competence and their conceptions about AI using 5-point Likert-type scales. In relation to AI competence, results indicate that affective attitudes predicted awareness and usage, leading to information avoidance and disengagement. Cognitive attitudes positively predicted AI awareness and usage. Behavioural attitudes, however, did not predict awareness or usage, suggesting that individuals may engage with AI technology without deeper understanding. For AI conceptions, behavioural attitudes were more closely linked to conceptions of AI in educational contexts. Positive behavioural attitudes predicted students' conceptions of AI's role in intelligent tutoring systems, retentions, drop-out reduction, recommendation systems, and personalised learning. In contrast, affective attitudes predicted conceptions of AI's use in classroom monitoring and performance prediction, while cognitive attitudes had little influence. These are areas educators can focus on when designing teaching & assessment strategies in relation to AI.