You are a crime scene investigator trying to match the lead content of bullet fragments found at a crime scene to the lead content of a box of bullets found with a suspect. To simplify this question, assume that the instrument you use gives you one measurement per fragment in grams/cm3. Assume that you have 5 measurements from fragments found at the crime scene and 7 measurements from bullets found with the suspect. (b) What are H0and Ha? Write them both mathematically and in words. (c) You run the analysis and the p-value is 0.0001 and α = 0.001, and β = 0.9. If you reject H0, what is the probability that you made the wrong decision in this case?
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!
You are a crime scene investigator trying to match the lead content of bullet fragments found at a crime scene to the lead content of a box of bullets found with a suspect. To simplify this question, assume that the instrument you use gives you one measurement per fragment in grams/cm3. Assume that you have 5 measurements from fragments found at the crime scene and 7 measurements from bullets found with the suspect.
(b) What are H0and Ha? Write them both mathematically and in words.
(c) You run the analysis and the p-value is 0.0001 and α = 0.001, and β = 0.9. If you reject H0, what is the
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