A sample of n=25 individuals is randomly selected from a population with a mean

Question

A sample of n=25 individuals is randomly selected from a population with a mean of 65, and a treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 70.
a. If the sample standard deviation is s = 10, are the data sufficient to conclude that the treatment has a significant effect using a two tailed test with mean =.05? Be sure to show all formulas with symbols (and plug in numbers), steps, processes and calculations for all parts of the answers (including how you arrived at the critical value).
b. If the sample standard deviation is s = 20, are the data sufficient to conclude that the treatment has a significant effect using a two tailed test with mean =.05? Be sure to show all formulas with symbols (and plug in numbers), steps, processes and calculations for all parts of the answers (including how you arrived at the critical value).

Explanation / Answer

Solution:

a) Given n = 25, df = n-1 = 24,  
= 0.05
the critical value = ± 2.064

t = [M- ]/[s/sqrt(n)] = [70 - 65]/[10/sqrt(25)]
= 2.5
Test statistic falls outside critical values, "Reject the null hypothesis is a significant treatment effect"

b) Given n = 25, df = n-1 = 24,  
= 0.05
the critical value = ± 2.064

t = [M- ]/[s/sqrt(n)] = [70 - 65]/[20/sqrt(25)]
= 1.25
Test statistic falls inside critical values, "Fail to reject the null hypothesis is a significant treatment effect"

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