Suppose a researcher is interested in investigating the effectiveness of a new medication aimed to treat HIV. The following table represents the CD4 cell count for a SRS of individuals treated with the new medication. Patient CD4 Patient CD4 Patient CD4 Count(cells/mm3) Count(cells/mm3) Count(cells/mm3) A 298 G 311 M 312 B 306 H 304 N 296 C 278 I 275 O 347 D 304 J 291 P 367 E 315 K 286 Q 275 F 320 L 333 R 281 A) Calculate the 95% CI for the average CD4 count in the population treated with the new medication, assuming that we can approximate with a normal distribution. Use a population standard deviation of 24.
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!
Suppose a researcher is interested in investigating the effectiveness of a new medication aimed to treat HIV. The following table represents the CD4 cell count for a SRS of individuals treated with the new medication.
Patient CD4 Patient CD4 Patient CD4 Count(cells/mm3) Count(cells/mm3) Count(cells/mm3)
|
A |
298 |
G |
311 |
M |
312 |
|
B |
306 |
H |
304 |
N |
296 |
|
C |
278 |
I |
275 |
O |
347 |
|
D |
304 |
J |
291 |
P |
367 |
|
E |
315 |
K |
286 |
Q |
275 |
|
F |
320 |
L |
333 |
R |
281 |
A) Calculate the 95% CI for the average CD4 count in the population treated with the new medication, assuming that we can approximate with a
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