A pharmaceutical company claims that its new drug reduces systolic blood pressure. The systolic blood pressure (in millimeters of mercury) for nine patients before taking the new drug and 22 hours after taking the drug are shown in the table below. Is there enough evidence to support the company's claim? Let d=(blood pressure before taking new drug)−(blood pressure after taking new drug)d=(blood pressure before taking new drug)−(blood pressure after taking new drug). Use a significance level of α=0.01α=0.01 for the test. Assume that the systolic blood pressure levels are normally distributed for the population of patients both before and after taking the new drug. Patient 1 2 3 4 5 6 7 8 9 Blood pressure (before) 198198 200200 159159 202202 185185 150150 148148 149149 175175 Blood pressure (after) 191191 174174 151151 178178 159159 140140 140140 141141 161161
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 pharmaceutical company claims that its new drug reduces systolic blood pressure. The systolic blood pressure (in millimeters of mercury) for nine patients before taking the new drug and 22 hours after taking the drug are shown in the table below. Is there enough evidence to support the company's claim?
Let d=(blood pressure before taking new drug)−(blood pressure after taking new drug)d=(blood pressure before taking new drug)−(blood pressure after taking new drug). Use a significance level of α=0.01α=0.01 for the test. Assume that the systolic blood pressure levels are normally distributed for the population of patients both before and after taking the new drug.
| Patient | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|
| Blood pressure (before) | 198198 | 200200 | 159159 | 202202 | 185185 | 150150 | 148148 | 149149 | 175175 |
| Blood pressure (after) | 191191 | 174174 | 151151 | 178178 | 159159 | 140140 | 140140 | 141141 | 161161 |
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