Question

1. The presence of harmful insects in farm fields is detected by erecting boards covered with a sticky material and then examining the insects trapped on the boards. To investigate which colors are most attractive to cereal leaf beetles, researchers placed six boards of each of four colors in a field of oats in July. The table below gives data on the number of cereal leaf beetles trapped:

Color	Insects Trapped
Yellow	45	59	48	46	38	47
White	21	12	14	17	13	17
Green	37	32	15	25	39	41
Blue	16	11	20	21	14	7

1. State hypotheses.

2. Run ANOVA test with 95% confidence level and fill in blanks.

SOURCE	SS	DF	MS	F	P	F crit
Between Groups
Within Groups
Total

From the F-ration and P-value, what conclusion can be drawn regarding the null hypothesis? Why?

Answer 1

Hypothesis:

Ha: At least one of the mean is different

CALCULATION:

Number of Treatment, t = 4 n = 24

T1 (sum of Yellow) = 283, T2(Sum of White) = 94, T3(Sum of Green) = 189, T3(Sum of Blue) = 89

G = Grand Total = 655

CF = Correction Factor = G2/N = 6552 / 24 = 17876.04

= 452 + 212 + ......................+ 72 - 17876.04

TSS = 5138.96

SSTR = (1 / 6) * [2832 + 942 + 1892 + 892] - 5138.96

SSTR = 4218.46

SSE = TSS - SSTR

= 5138.96 - 4218.46

SSE = 920.50

MSSTR = SSTR/t-1 = 4218.46 / 4-1 = 1406.153

MSSE = SSE / n-t = 920.50 /24-4 = 46.025

F = MSSTR / MSSE = 1406.153 / 46.025 = 30.55

Ftabulate = F,(t-1,n-t) = F0.05,(3,20) = 3.0984                            ..............Using F table

P-value = 0.0000

ANOVA TABLE:

Conclusion:

P-value < , i.e. 0.0000 < 0.05, That is Reject Ho at 5% level of signifiance.

Reject Null Hypothesis, There is evidence that some colors attract more leaf beetles than other.