To evaluate the effect of a treatment, a sample of n = 9 is obtained from a popu
ID: 2960182 • Letter: T
Question
To evaluate the effect of a treatment, a sample of n = 9 is obtained from a population with a mean of µ = 40, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 33.a. If the sample has a standard deviation of s = 9, are the data sufficient to conclude that the treatmenthas a significant effect using a two-tailed test with a .05?
b. If the sample standard deviation is s = 15, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with a .05?
c. Comparing your answer for parts a and b, how does the variability of the scores in the sample influence the outcome of a hypothesis test?
Explanation / Answer
Given µ = 40, n=9, xbar=M=33
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a. If the sample has a standard deviation of s = 9, are the data sufficient to conclude that the treatmenthas a significant effect using a two-tailed test with a .05?
The test hypothesis is
Ho:=40
Ha: not equal to 40
The test statistic is
t=(xbar- )/(s/n)
=(33-40)/(9/3)
= -2.33
Given a=0.05, the critical value is t(0.025, df=n-1=8)= -2.31 (check student t table)
Since t=-2.33 > -2.31, we reject Ho. So we can conclude that the treatment has a significant effect.
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b. If the sample standard deviation is s = 15, are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with a .05?
The test hypothesis is
Ho:=40
Ha: not equal to 40
The test statistic is
t=(xbar- )/(s/n)
=(33-40)/(15/3)
= -1.4
Given a=0.05, the critical value is t(0.025, df=n-1=8)= -2.31 (check student t table)
Since t=-1.4 > -2.31, we do not reject Ho. So we can not conclude that the treatment has a significant effect.