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=0.05α=0.05 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) 156156 155155 167167 176176 191191 160160 159159 197197 181181 Blood pressure (after) 146146 144144 154154 161161 165165 146146 148148 171171 155155 Copy Data Step 1 of 5 : State the null and alternative hypotheses for the tes
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=0.05α=0.05 for the test. Assume that the systolic blood pressure levels are
| Patient | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|
| Blood pressure (before) | 156156 | 155155 | 167167 | 176176 | 191191 | 160160 | 159159 | 197197 | 181181 |
| Blood pressure (after) | 146146 | 144144 | 154154 | 161161 | 165165 | 146146 | 148148 | 171171 | 155155
Copy Data Step 1 of 5 :
State the null and alternative hypotheses for the test. |
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