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**Mathsdog** Hi Wevans, The null hypothesis is that the initial supposition is true, in this case that bike hire is on average < 60 minutes. If your data supported this supposition then you would have no evidence to reject the null hypothesis. Its not so much a question of which hypothesis you want to reject as it is asking: what is the probability (p-value) that two samples come from the same distribution (the null hypothesis)? Or in your case, the probability that your data (sample) comes from a population (all hires) whose true mean is < 60 mins. If this probability is very low (usually taken to be a probability< 0.05, arbitrarily I might add) then this is taken as evidence that the samples come do not come from the same distribution. Notice that at this p-value threshold (0.05) one in twenty times when samples do come from the same distribution you will incorrectly reject the null hypothesis. Hence why the smaller your p-value is the stronger is the evidence for rejecting the null.

Be careful to distinguish between a sample and a population. If you have all the data for all bike-hires, then there is no "test" to do; simply calculate the population mean. It is what it is. If however you only have a sample, the question is whether this is representative of the true population. This is the root of much controversy in medical statistics, since it is very easy to select an unrepresentative sample from the population and very hard to select a representative one.

I hope that is a bit clearer. MD