A professor is interested in whether there is a gap in counseling students' statistics competency scores between 1) those who have never taken any statistics course, 2) those who have only taken an undergraduate statistics course, 3) those who have taken COUN 503, and 4) those who have takenan advanced statistic course whereas working on a Ph. D. The professor gathers information from a random sample of students and obtains the statistics competency scores. The scoresare normally distributed.
1)
2)
3)
4)
7
11
13
15
6
14
8
10
5
12
4
a. What statistical test should be used to examine these data?
b. Identify H_{0} and H_{a} for this study.
c. Conduct the exactly analysis.
d. Should H_{0} be rejected? What should the researcher conclude?