Cobra Cheese Company buys milk from several suppliers. Cobra suspects that some producers are adding water to their milk to increase their profits. Excess water can be detected by measuring the freezing point of the milk. The freezing temperature of natural milk varies according to a normal distribution, with mean μ = 31.019° and standard deviation σ = 0.014°. Added water raises the freezing temperature toward 32°, the freezing point of water. Cobra's laboratory manager measures the freezing temperature of a random sample of 5 lots of milk from one producer. The mean measurement is = 31.032°. Is this good evidence that the producer is adding water to the milk? State hypotheses, identify the test statistic, give the P-value, and state your conclusion. In stating your conclusions, answer the following questions: Is there significant evidence (at the 5% level) that the freezing point of the milk is higher than 31.019°?
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!
Cobra Cheese Company buys milk from several suppliers. Cobra suspects
that some producers are adding water to their milk to increase their
profits. Excess water can be detected by measuring the freezing point of the
milk. The freezing temperature of natural milk varies according to a normal
distribution, with mean μ = 31.019° and standard deviation σ = 0.014°. Added
water raises the freezing temperature toward 32°, the freezing point of
water. Cobra's laboratory manager measures the freezing temperature of a
random sample of 5 lots of milk from one producer. The mean measurement is
= 31.032°. Is this good evidence that the producer is adding water to the
milk? State hypotheses, identify the test statistic, give the P-value, and
state your conclusion. In stating your conclusions, answer the following
questions:
Is there significant evidence (at the 5% level) that the freezing point
of the milk is higher than 31.019°?
In plain language, what should you tell the cheese factory?
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