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 board. 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
Lemon 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
a. Is there a significant difference in the average numbers of leaf beetles trapped among the 4 colors? The level of significance is set at 5%. Please carry out the hypothesis testing by setting up null and alternate hypothesis. 𝐻_0: 𝜇_1=𝜇_2=𝜇3= . . . =𝜇𝑘 𝐻_𝑎: At least one mean is different from the others
F^stat > F^critical= Reject H_0 30.55 > 3.10 = Reject H_0
b. If the null hypothesis is rejected in part (a), what can you further conclude as to which group(s) has different averages than others? However, it the null hypothesis is not rejected in part (a), what does it mean in the context of the problem.
Above is the question that I'm trying to solve. I came up with the hypothesis and concluded rejecting H_0, however now I'm stuck here and not sure what to do now. I'm thinking that I need to do a pooled T-test but don't know the formula for a One-way ANOVA pooled T-test. Also, whenever I get my number from the pooled T-test how will this help me to tell if the means are different?
If anyone can help I'd really appreciate it. I'm not just looking for the answer I want to be able to better understand how to solve these types of questions and I've looked into tutoring but my college doesn't have anyone to help tutor for stats so now I'm looking for any help, thanks again.