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.
a) n = 16
Since observed z < z0.025 hence the treatment does not have a significant effect.
b) n = 36
Since observed z > z0.025 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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