Your company uses a very expensive machine to manufacture nuclear fuel rods. The production process using this machine has been refined so that only an average of 3 millirads of radiation/week is emitted during the production process. The standard deviation of radiation during the process is known to be, σ = .251179 millirads/week. The machine has recently undergone an overhaul. Your job is to report on the average radiation/week this machine is now producing. Any deviation from 3 millirads/week is of great concern. You conduct a sample of 7 weeks of production and compute a sample mean of 2.85 millirads of radiation/week. You can assume the amount of radiation produced during production is a normally distributed random variable and the population standard deviation is still σ = .251179 millirads of radiation/week. State the null and alternative hypothesis.
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!
Your company uses a very expensive machine to manufacture nuclear fuel rods. The production process using this machine has been refined so that only an average of 3 millirads of radiation/week is emitted during the production process. The standard deviation of radiation during the process is known to be, σ = .251179 millirads/week. The machine has recently undergone an overhaul. Your job is to report on the average radiation/week this machine is now producing. Any deviation from 3 millirads/week is of great concern. You conduct a sample of 7 weeks of production and compute a sample mean of 2.85 millirads of radiation/week. You can assume the amount of radiation produced during production is a normally distributed random variable and the population standard deviation is still σ = .251179 millirads of radiation/week.
State the null and alternative hypothesis.
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