Question

To detect the presence of harmful insects in farm fields, we can put up boards covered with a sticky material and examine the insects trapped on the boards. Which colors attract insects best? Experimenters placed six boards of each of four colors at random locations in a field of oats and measured the number of cereal leaf beetles trapped. Conduct a one-way ANOVA

Conduct a hypothesis test using the One Way ANOVA approach to compare the null hypothesis that all means are equal versus at least two means are not equal. Use a type 1 error rate of 5%. Write down all steps in the hypothesis testing process and define the parameters under the null and alternative hypotheses.

Blue	Green	White	Red
16	37	21	45
11	32	12	59
20	20	14	48
21	29	17	46
14	37	13	38
7	32	20	47

Answer 1

Step One: State the Hypotheses

Let be the average of number of cereal leaf beetles trapped in all groups.

Step Two: Calculate the Test Statistic

Enter data in excel.

Click on Data->Data Analysis->One way ANOVA

Enter data in data range, click OK.

The output is shown below:

The test statistic is F=42.84

Step Three: Find the P-value

From the above output, p-value=0.0000

Step Four: Decision (compare the p-value to alpha)

Since p-value=0.0000 is less than type 1 error rate of 5% (0.05), we reject the null hypothesis.

Step Five: Conclusion (be sure this is in complete sentence form)

We can conclude that at least two groups have different means.