Choppies Supermarket believes that customers to its stores spend half an hour, on average, doing their purchases in their store. The consumer watchdog wants to verify this claim. To do this they observe the entry and departure times of 86 randomly selected customers from random Choppies supermarkets. The sample average time in the store was 27.9 minutes. Assume a population standard deviation of 10.5 minutes and that shopping time is approximately normally distributed. (a) Formulate the null and alternative hypotheses for this test scenario. [2] (b) Test the validity of the supermarket's belief by conducting a hypothesis test using a=0.1. Conclude from your observations [8]