to evaluate the effect of a treatment, a sample of n=9 is obtained from a popula

Question

to evaluate the effect of a treatment, a sample of n=9 is obtained from a population with a mean of =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 treatment has a significant effect using a two-tailed test with =0.05?

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 =0.05?

c) comparing your answer for part a and b, how does the variability of the scores is the sample infuence the outcome of a hypothesis test?

Explanation / Answer

a)
Critical t at a=0.05 for 8 df, two-tailed: 2.036
(because the area under the t-distribution curve to the right of 2.036 plus the area to the left of -2.036 is 0.05)
sd of sample mean = s/sqrt(n) = 9/sqrt(9) = 3
t = (40-33)/3 = 2.33
Yes, the treatment has a significant effect (since 2.33 > 2.036)

b)
sd of sample mean = s/sqrt(n) = 15/sqrt(9) = 5
t = (40-33)/5 = 1.2
No, we cannot conclude that the treatment has a significant effect since 1.2 < 2.036

c) The null hypothesis is rejected when sample variability is smaller.

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