To check on an ambulance service’s claim that at least 40% of its calls are life-threatening emergencies, a random sample was taken from its files, and it was found that only 49 of 150 calls were life-threatening emergencies. Can the null hypothesis p = 0.40 be rejected against the alternative hypothesis p < 0.40 if the probability of a Type I error is to be at most 0.01?

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Random Variables

A random variable Z is a real valued function of the type Z: S → R on a sample space S. That means the function assigns a real number to every primitive event in the sample space. In other words, a random variable is a function mapping a sample space S to a set of real numbers R.