Question 1

power.t.test(n = NULL, delta = 0.015, sig.level = 0.05, type = c("paired"),  power = 0.75, alternative = c("one.sided"), sd = 0.03 )
## 
##      Paired t test power calculation 
## 
##               n = 22.92961
##           delta = 0.015
##              sd = 0.03
##       sig.level = 0.05
##           power = 0.75
##     alternative = one.sided
## 
## NOTE: n is number of *pairs*, sd is std.dev. of *differences* within pairs

Comment: The total number of samples to assess the bioavailability of the drug would be 23 samples. This would equate to 44 samples with two coming from each person.

Question 2

library(pwr)
?pwr.t.test
## starting httpd help server ... done
pwr.t.test(n = NULL, power = 0.85 ,sig.level = 0.1,type = c("two.sample"), d = -0.5, alternative = c('less'))
## 
##      Two-sample t test power calculation 
## 
##               n = 43.40568
##               d = -0.5
##       sig.level = 0.1
##           power = 0.85
##     alternative = less
## 
## NOTE: n is number in *each* group

Comment: The amount of samples to determine if active exercise can shorten the time for an infant to learn how to walk would be 44 samples from each group.

#Complete Code

power.t.test(n = NULL, delta = 0.015, sig.level = 0.05, type = c("paired"),  power = 0.75, alternative = c("one.sided"), sd = 0.03 )

library(pwr)
?pwr.t.test
pwr.t.test(n = NULL, power = 0.85 ,sig.level = 0.1,type = c("two.sample"), d = -0.5, alternative = c('less'))