A pharmaceutical company produces pills of dose level of 40 mg. To maintain the quality control, the average weight of all pills needs to be 40 mg and the st. dev. 0.4 mg. A sample of 25 pills yielded the sample mean of 39.5 mg. Test the hypothesis at that the average weight of the pills has changed. Assume that the weights of the pills follow normal distribution. You must state the null and the alternative hypotheses.
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 pharmaceutical company produces pills of dose level of 40 mg. To maintain the quality control, the average weight of all pills needs to be 40 mg and the st. dev. 0.4 mg. A sample of 25 pills yielded the sample
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