Question

**A random sample is selected from a normal population
with a mean of μ=50 and a standard deviation of σ=12. After a
treatment is administered to the individuals in the sample, the
sample mean is found to be M=55.**

**a. If the sample consists of n=16 scores, is the sample
mean sufficient to conclude that the treatment has a significant
effect? Use a two-tailed test with α =0.05. b. If the sample
consists of n=36 scores, is the sample mean sufficient to conclude
that the treatment has a significant effect? Use a two-tailed test
with α =0.05. c. Compare your answers for parts a and b, explain
how the size of the sample influences the outcome of a hypothesis
test.**

Answer #1

a) n = 16

Since observed z < z_{0.025} hence the treatment does
not have a significant effect.

b) n = 36

Since observed z > z_{0.025} hence the treatment have
a significant effect.

c) We see as the size of the sample increases the effect of the treatment administered also increases. At first we selected only 16 samples and the treatment is administered on them. It may happen that these 16 individuals does not respond properly. Instead if we keep on increasing the sample size the test may come to be more effective.

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