A new vitamin supplementation program is intended to decrease average resting heart rate in individuals at risk for hypertension. Assume that a team of researchers are hopeful that resting heart rate in their population will get down to less than 68 bpm, in a population with a standard deviation of 2 bpm. In order to test this goal reduction, the team gathers a SRS of 273 participants in their program and calculates a sample average resting heart rate of 74 bpm. A) Carry out a one sample Z test to determine if the team can conclude that the supplementation program is successful in meeting their goal reduction in resting heart rate. Use an α=0.05. Construct a 95% Confidence interval about the sample mean, and interpret the result.
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!
A new vitamin supplementation program is intended to decrease average resting heart rate in individuals at risk for hypertension. Assume that a team of researchers are hopeful that resting heart rate in their population will get down to less than 68 bpm, in a population with a standard deviation of 2 bpm. In order to test this goal reduction, the team gathers a SRS of 273 participants in their program and calculates a sample average resting heart rate of 74 bpm.
A) Carry out a one sample Z test to determine if the team can conclude that the supplementation program is successful in meeting their goal reduction in resting heart rate. Use an α=0.05. Construct a 95% Confidence interval about the sample mean, and interpret the result.
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