Answer to Question #153368 in Statistics and Probability for sara

Question

Many college and university students

obtain summer jobs. A statistics professor wanted

to determine whether students in different degree

programs earn different amounts. A random sample

of 5 students in the B.A., B.Sc., and B.B.A. programs

were asked to report what they earned the

previous summer. The results (in $1,000s) are listed

here. Can the professor infer at the 5% significance

level that students in different degree programs differ

in their summer earnings?

B.A. B.Sc. B.B.A.

3.3 3.9 4.0

2.5 5.1 6.2

4.6 3.9 6.3

5.4 6.2 5.9

3.9 4.8 6.4

Answer 1

H₀: μ₁ = μ₂ = μ₃

H₁: At least two means are differ

A One-Way ANOVA test was conducted at α = 0.05; the Excel output is provided below.

The F value calculated 3.91 > critical value F(crit) of 3.78. The probability to obtain this result by chance (P-value) was calculated as 0.048 or 4.8 %. So, we are able to conclude that there was significant difference in average between summer earnings of students in different degree programs.