Question 1

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

We need at least 23 participants.

Question 2

alpha=0.10
power=0.85
d=0.5
library("pwr")
pwr.t.test(n=NULL, d=0.5, sig.level = 0.10, power = 0.85, type = c("two.sample"), alternative = c("greater"))
## 
##      Two-sample t test power calculation 
## 
##               n = 43.40568
##               d = 0.5
##       sig.level = 0.1
##           power = 0.85
##     alternative = greater
## 
## NOTE: n is number in *each* group

We need at least 44 participants in each group. In total we need 88.

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

alpha=0.10
power=0.85
d=0.5
library("pwr")
pwr.t.test(n=NULL, d=0.5, sig.level = 0.10, power = 0.85, type = c("two.sample"), alternative = c("greater"))