The problem of causally scheduling power consumption to minimize the expected cost at the consumer side is considered. The price of electricity is assumed to be time-varying. The scheduler has access to past and current prices, but only statistical knowledge about future prices, which it uses to make an optimal decision in each time period. The scheduling problem is naturally cast as a Markov decision process. Algorithms to find decision thresholds for both noninterruptible and interruptible loads under a deadline constraint are then developed. Numerical results suggest that incorporating the statistical knowledge into the scheduling policies can result in significant savings, especially for short tasks. It is demonstrated with real price data from Commonwealth Edison that scheduling with mismatched modeling and online parameter estimation can still provide significant economic advantages to consumers.