To evaluate the effect of a treatment, a sample of n=8 is obtained from a popula

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.

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