nfortunately, arsenic occurs naturally in some ground water†. A mean arsenic level of μ = 8.0 parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 31 tests gave a sample mean of x = 7.1 ppb arsenic, with s = 2.3 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use ? = 0.05. What is the level of significance? What is the value of the sample test statistic? (Round your answer to three decimal places.) Find the P-value. (Round your answer to four decimal places.)
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!
Unfortunately, arsenic occurs naturally in some ground water†. A mean arsenic level of μ = 8.0 parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 31 tests gave a sample mean of x = 7.1 ppb arsenic, with s = 2.3 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use ? = 0.05.
What is the level of significance?
What is the value of the sample test statistic? (Round your answer to three decimal places.)
Find the P-value. (Round your answer to four decimal places.)
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