A hospital administrator finds that the mean hospital stay for a sample of 77 women after childbirth is 3.1 days. She claims that the mean stay at her hospital is greater than the national average of 2.7 days. Assuming that the average at her hospital is the same as the national average, the probability of observing a sample with a mean of 3.1 days or more is 0.16. Formulate the null and alternative hypotheses. Then discuss whether the sample provides evidence for rejecting or not rejecting the null hypothesis. Assume a significance level of 0.05
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
A hospital administrator finds that the mean hospital stay for a sample of 77 women after childbirth is 3.1 days. She claims that the mean stay at her hospital is greater than the national average of 2.7 days. Assuming that the average at her hospital is the same as the national average, the
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