1. A manufacturer of salad dressings uses machines to dispense liquid ingredients into bottles that move along a filling line. The machine that dispenses dressing is working properly when 8 ounces are dispensed. The manufacturer is particularly concerned that the bottles do not have an average of less than 8 ounces. The standard deviation of the process is 0.15 ounce. A sample of 50 bottles is selected. Suppose that the average amount dispensed in a particular sample of 50 bottles is 7.983 ounces. a. State the null and alternative hypotheses b. At the 0.05 level of significance, is there evidence that the mean amount dispensed is less than 8 ounces
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!
1. A manufacturer of salad dressings uses machines to dispense liquid ingredients into bottles that move along a filling line. The machine that dispenses dressing is working properly when 8 ounces are dispensed. The manufacturer is particularly concerned that the bottles do not have an average of less than 8 ounces. The standard deviation of the process is 0.15 ounce. A sample of 50 bottles is selected. Suppose that the average amount dispensed in a particular sample of 50 bottles is 7.983 ounces.
a. State the null and alternative hypotheses
b. At the 0.05 level of significance, is there evidence that the mean amount dispensed is less than 8 ounces.
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