For normal population mean 60, standard deviation 15, after treatment is given to the member of sample , the sample mean is 65, and sample size is 25.

Question

For normal population mean 60, standard deviation 15, after treatment is given to the member of sample , the sample mean is 65, and sample size is 25.
 is the sample mean sufficient to conclude that the treatment has significant effect? Give reason for decision?

PsyDAG · Answer

Z = (mean1 - mean2)/standard error (SE) of difference between means

SEdiff = √(SEmean1^2 + SEmean2^2)

SEm = SD/√n

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 the Z score. Is that less than the level of significance you are using?