Question

A statistics instructor wonders whether significant differences exist in her students’ final exam scores in her three different sections. She randomly selects the scores from 10 students in each section. A portion of the data is shown in the accompanying table. Assume exam scores are normally distributed.

Section 1	Section 2	Section 3
82	50	72
76	51	79
63	59	96
90	76	86
61	74	54
79	50	86
56	73	78
59	63	83
79	84	95
89	78	95

Construct an ANOVA table. (Round "Sum Sq" and "Mean Sq" to 1 decimal place, "F value" to 3, and "p-value" to 3 decimal places. Before fitting your model, type options(scipen=10) and options(digits=10) into your R console.)

ANOVA
Source of Variation	Df	Sum Sq	Mean Sq	F value	Pr(>F)
Section
Residuals

Answer 1

Solution:

We can use R to find the ANOVA values. The R code and output is given below:

R-Code:

options(scipen=10)
options(digits=10)
Section_1 <-c(82,76,63,90,61,79,56,59,79,89)
Section_2 <-c(50,51,59,76,74,50,73,63,84,78)
Section_3 <-c(72,79,96,86,54,86,78,83,95,95)
combined_groups<-data.frame(cbind(Section_1,Section_2,Section_3))
stacked_groups<-stack(combined_groups)
Anova_Results<-aov(values ~ind, data=stacked_groups)
summary(Anova_Results)

The R-output is given below:

Therefore, the ANOVA table is: