Question: A random sample of 30 offshore oil workers took part in a simulated escape exercise resulting in data on time (in seconds) to complete the escape. The data from the escape times of these 30 workers have a sample mean of 370 seconds and a sample standard deviation of 44 seconds. The investigators belief, prior to the study, was that the average escape time is not greater than 6 minutes.

1. State the relevant null and alternative hypotheses, in terms of a suitable parameter, in order to answer the following question: Is there enough evidence to suggest that the belief of the investigators is unjustified?
2. Write down a formula for the relevant test statistic. What is its (approximate) distribution given that the null hypothesis is true?
3. Carry out the relevant test. specifying the critical region (use a = 0.05) and state clearly the conclusion from the test.

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