Question

Use PROC GLM in SAS to test whether the mean number of insect deaths differs across insectide 
types.  Use alpha= 0.05, and justify your answer by referring to either a test statistic value 
and table value, or by referring to a P-value.

data insectdeaths; 
input INSECTICIDE $  DEAD;
cards;
 A 85
 B 90
 C 93
 D 98
 A 82
 B 92
 C 94
 D 98
 A 83
 B 90
 C 96
 D 100
 A 88
 B 91
 C 95
 D 97
 A 89
 B 93
 C 96
 D 97
 A 92
 B 81
 C 94
 D 99
;
run;

Answer 1

Treat insecticides as a grouping variable using class statement in proc glm

use model statement  

Ho:

he mean number of insect deaths are same across insectide 
types. 

Ha:

The mean number of insect deaths differs across insectide 
types. 

SAS code:

data insectdeaths;
input INSECTICIDE $ DEAD;
cards;
A 85
B 90
C 93
D 98
A 82
B 92
C 94
D 98
A 83
B 90
C 96
D 100
A 88
B 91
C 95
D 97
A 89
B 93
C 96
D 97
A 92
B 81
C 94
D 99
;
run;
proc glm data = insectdeaths;
class INSECTICIDE ;
model DEAD = INSECTICIDE ;
means INSECTICIDE ;
run;

Output;

The GLM Procedure

Class Level Information
Class	Levels	Values
INSECTICIDE	4	A B C D

Number of Observations Read	24
Number of Observations Used	24

The GLM Procedure

Dependent Variable: DEAD

Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	3	488.7916667	162.9305556	17.99	<.0001
Error	20	181.1666667	9.0583333
Corrected Total	23	669.9583333

R-Square	Coeff Var	Root MSE	DEAD Mean
0.729585	3.264029	3.009707	92.20833

Source	DF	Type I SS	Mean Square	F Value	Pr > F
INSECTICIDE	3	488.7916667	162.9305556	17.99	<.0001

Source	DF	Type III SS	Mean Square	F Value	Pr > F
INSECTICIDE	3	488.7916667	162.9305556	17.99	<.0001

The GLM Procedure

Level of INSECTICIDE	N	DEAD
		Mean	Std Dev
A	6	86.5000000	3.83405790
B	6	89.5000000	4.32434966
C	6	94.6666667	1.21106014
D	6	98.1666667	1.16904519

since F=17.99,p<.0001,

p<0.05

Reject Ho that all the 4 type insecticides means are equal

and conclude that there is sufficient evidence at 5% level of significance that

he mean number of insect deaths differs across insectide 
types.