A coffee packaging plant claims that the mean weight of coffee in its containers is at least 32 ounces. A random sample of 15 containers were weighed and the mean weight was 31.8 ounces with a sample standard deviation of 0.48 ounces. At the 0.01 significance level, test the claim that the mean weight is at least 32 ounces. Assume a normal distribution and complete the test below. Remember, since this is a study of the mean, use the t-distribution Ho; µ> 32 НА; и < 32 The critical value is (round to 3 decimals) The test statistic is (round to 3 decimals) Does the data support or not support the claim (type in support or does not support)
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!
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