The paper "Trends in Blood Lead Levels and Blood Lead Testing among U.S. Children Aged 1 to 5 Years"t gave data on blood lead levels (in mg/dL) for samples of children living in homes that had been classified either at low, medium, or high risk of lead exposure, based on when the home was constructed. After using a multiple comparison procedure, the authors reported the following. 1. The difference in mean blood lead level between low-risk housing and medium-risk housing was significant. 2. The difference in mean blood lead level between low-risk housing and high-risk housing was significant. 3. The difference in mean blood lead level between medium-risk housing and high-risk housing was significant. Which of the following sets of T-K intervals (Set 1, 2, or 3) is consistent with the authors' conclusions? Explain your choice. H2 = mean blood lead level for children living in low-risk housing = mean blood lead level for children living in mediumrisk housing HH = mean blood lead level for children living in high-risk housing Difference Set 1 Set 2 Set 3 (-0.6, 0.1) (-0.6, -0.1) (-0.6, -0.1) (-1.5, -0.6) (-1.5, -0.6) (-1.5, -0.6) HM - HH (-0.9, -0.3) (-0.9, 0.3) (-0.9, -0.3) Set 2 is consistent with the author's conclusions because some of the given intervals in that set contain zero. Set 1 is consistent with the author's conclusions because none of the given intervals in that set contain zero. Set 2 is consistent with the author's conclusions because none of the given intervals in that set contain zero. O Set 3 is consistent with the author's conclusions because none of the given intervals in that set contain zero. Set 1 is consistent with the author's conclusions because some of the given intervals in that set contain zero. Set 3 is consistent with the author's conclusions because some of the given intervals in that set contain zero. O O O O O O

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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!