Question

According to government records, the starting salary for an individual with a BA degree in Liberal Arts in 2010 was $35,000 with a standard deviation of $5,000. A researcher at a small liberal arts college wants to see if the graduates at his college had higher starting salaries than the national average. A random sample of 25 students who graduated in 2010 reveals that their average starting salary was, X = $38,000.

Using the data, suppose the true mean salary for the small college liberal arts graduates was $37,000.
a. How much power would the researcher have to reject the false null hypothesis using the

sample size of n = 25 and ? = .01?
b. What would be the probability of making a Type II Error?

c. Calculate the effect size for problem 7.

Answer 1

a) First we need to compute Xbar(critical)

Z = xbar - mu / sd

2.576 = xbar - 35000 / (5000/sqrt(25))

xbar = 37576

Now we compute probability of > 37576

p(x > 37576) = p ( Z > 37576 - 37000/1000) = p(Z > 0.576) = 0.2823

This test is two tailed,

So power of test is = 1 - 2*0.2823 = 0.4354

b) Type II error = 1 - 0.4354 = 0.5646

c) first we need to compute Cohen's D

D = (xbar - mu) / sd = 38000 - 35000) / 1000 = 3

It is large effect and mean difference is 3 standard deviations.