Question

A sample of 16 students took the American College Testing (ACT) Program composite college entrance exam and were found to have a mean of 18 and a sample SD equal to 6. (A) What is the value of the estimated standard error of the mean (SEM)? (B) Provide an interpretation of the value obtained in part A. (C) Describe how the researcher might reduce the size of the SEM if the study is repeated.

Answer 1

(A)

Standard Error of the mean (SEM) is given by:

SEM = s/

= 6/ = 1.5

So,

Answer is:

1.5

(B)

Interpretation of SEM = 1.5:

Standard error of the mean (SEM) = 1.5 provides a rough estimate of the interval in which the population mean () is likely to fall. SEM permits the researcher to construct a Confidence Interval in which the population mean is likely to fall.

(C) The researcher might reduce the size of the SEM if the study is repeated by increasing the Sample Size (n).