GPA and major. Undergraduate students taking an introductory statistics course at Duke University conducted a survey about GPA and major. The side-by-side box plots show the distribution of GPA among three groups of majors. Also provided is the ANOVA output.
G PA
Arts and Humanities Natural Sciences Social Sciences
2.5
3.0
3.5
4.0
Df Sum Sq Mean Sq F value Pr(>F)
major 2 0.03 0.015 0.185 0.8313 Residuals 195 15.77 0.081
(a) Write the hypotheses for testing for a difference between average GPA across majors.
(b) What is the conclusion of the hypothesis test?
(c) How many students answered these questions on the survey, i.e. what is the sample size?