A researcher wants to compare the mean concentration of two medications considered biologically equivalent, i.e., two medications that are able to produce the same therapeutic effect at the same level of concentration in the blood. The group of individuals on medication one (n = 32) had a mean blood concentration of 21.7 micrograms per milliliter with a standard deviation of 8.7 micrograms per milliliter. The group of individuals on medication two (n= 32) had a mean blood concentration of 19.4 micrograms per milliliter with a standard deviation of 5.2 micrograms per milliliter. Construct and interpret a 95% confidence interval demonstrating the difference in means for the individuals on medication one when compared to the group of individuals on medication two. The researchers are 95% confident that the true mean difference in medication concentration levels between individuals on medication one and individuals on medication two is between 4.867 micrograms per milliliter and 9.467 micrograms per milliliter. The researchers are 95% confident that the true mean difference in medication concentration levels between individuals on medication one and individuals on medication two is between -1.212 micrograms per milliliter and 5.812 micrograms per milliliter. The researchers are 95% confident that the true mean difference in medication concentration levels between individuals on medication one and individuals on medication two is between 11.747 micrograms per milliliter and 16.347 micrograms per milliliter. The researchers are 95% confident that the true mean difference in medication concentration levels between individuals on medication one and individuals on medication two is between 3.477 micrograms per milliliter and 8.077 micrograms per milliliter.
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 researcher wants to compare the
= 32) had a mean blood concentration of 19.4 micrograms per milliliter with a standard deviation of 5.2 micrograms per milliliter. Construct and interpret a 95% confidence interval demonstrating the difference in means for the individuals on medication one when compared to the group of individuals on medication two.
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The researchers are 95% confident that the true mean difference in medication concentration levels between individuals on medication one and individuals on medication two is between 4.867 micrograms per milliliter and 9.467 micrograms per milliliter. |
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The researchers are 95% confident that the true mean difference in medication concentration levels between individuals on medication one and individuals on medication two is between -1.212 micrograms per milliliter and 5.812 micrograms per milliliter. |
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The researchers are 95% confident that the true mean difference in medication concentration levels between individuals on medication one and individuals on medication two is between 11.747 micrograms per milliliter and 16.347 micrograms per milliliter. |
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The researchers are 95% confident that the true mean difference in medication concentration levels between individuals on medication one and individuals on medication two is between 3.477 micrograms per milliliter and 8.077 micrograms per milliliter. |
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