To evaluate the effect of a treatment, a sample of n=8 is obtained from a popula
ID: 3340940 • Letter: T
Question
To evaluate the effect of a treatment, a sample of n=8 is obtained from a population with a mean of m=40, and the treatment is administered to the individual in the sample. After treatment, the sample mean is found to be M=35.
A if the sample variance is s2=32, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with a=.05?
B If the sample variance is s2=72, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with a=.05?
C comparing your answers for parts a and b, how does the variability of the scores in the sample influence the outcome of a hypothesis test?
Please show work.
Explanation / Answer
Ans:
a)
sample vraiance=32
sample standard dev,s=sqrt(32)
Standard error=s/sqrt(n)=sqrt(32/8)=2
critical t value for alpha=0.05 and df=8-1=7 is +/-2.365
t=(35-40)/2=-5/2=-2.5
As,t=-2.5<-2.365,we reject null hypothesis.
hence,data is sufficient to conclude that the treatment has a significant effect.
b)
now,
standard error=sqrt(72/8)=3
t=(35-40)/3=-5/3=-1.67
As,t=-1.67>-2.365,we fail to reject null hypothesis.
hence,data is not sufficient to conclude that the treatment has a significant effect.
c)As,sample variance is increased,standard error is increased,and t statistic decreased,so we are less likely to reject null hypothesis and less likely to conclude that the treatment has significant effect.