For each of the following samples that were given an experimental treatment test whether these samples represent populations that are different from the general population (a) a sample of 10 with a mean of 44, (b) a sample of 1 with a mean of 48. The general population of individuals has a mean of 40, a standard deviation of 6, and follows a normal curve. For each sample carry out a Z test using the five steps hypothesis testing with a two-tailed test at the .05 significance level.
* Use the formula (xbar-x)/ (s/sqrtn) If the answer is larger than 2 reject HO, If the answer is smaller than 2 then do not reject HO.
a. Z = (mean1 - mean2)/standard error (SE) of difference between means
SEdiff = √(SEmean1^2 + SEmean2^2)
SEm = SD/√(n-1)
If only one SD is provided, you can use just that to determine SEdiff.
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to your Z score.
b. Sample of one is just like an individual score.
Z = (score-mean)/SD Use same table.
What if the answer is exactly 2?