Assignment 5 Group 6

Question 1 Solution

• Same person (paired test)

• \[\sigma = 0.03\]

• \[\alpha = 0.05\]

• Power = 75%

• \[\mu _{a} - \mu _{b} = 15%\]

\[ \mu _{a} - \mu _{b} > 0 \] \[ d = \frac{\mu _{a} - \mu _{b}}{\sigma } \]

#intsalling power library
library(pwr)
#number of samples for paired t-test
d<-0.015/0.03
pwr.t.test(n=NULL,d=d,sig.level=0.05,power=.75,type="paired",alternative="greater")

## 
##      Paired t test power calculation 
## 
##               n = 22.92958
##               d = 0.5
##       sig.level = 0.05
##           power = 0.75
##     alternative = greater
## 
## NOTE: n is number of *pairs*

The number of samples we need to collect data such that there would be 75% chance of correctly rejecting the null hypothesis if the urine concentration of Aspirin B is 1.5% less than that of Aspirin A is 23.

Question 2 Solution

• Two sample test (independent)

• = 10%

• Power = 85%

• Effect size = 50%

#intsalling power library
library(pwr)
#number of samples for 2-Sample t-test,
pwr.t.test(n=NULL,d=.5,sig.level=0.10,power=.85,type="two.sample")

## 
##      Two-sample t test power calculation 
## 
##               n = 58.20169
##               d = 0.5
##       sig.level = 0.1
##           power = 0.85
##     alternative = two.sided
## 
## NOTE: n is number in *each* group

• How many infants do they need to enroll in each group?

  • For each group, they need to enroll 59 infants.

• How many total??

  • In total, 118 infants will be needed to enroll.