Question

Please walk me through SPSS setup for this and complete the following:

Consider the data below of inches of rainfall per month for three different regions in the Northwestern United States: Please use SPSS and complete the following:

Plains Mountains. Forest

April 25.2. 13.0 9.7

May 17.1 18.1 16.5

June 18.9. 15.7. 18.1

July 17.3 11.3 13.0

August 16.5 14.0 15.4

Using SPSS, perform an ANOVA test for the hypothesis that there is not the same amount of rainfall in every region in the Northwestern United States with a significance level of 0.02. What are the two degrees of freedom of your test statistic? Please attach your Word file and, in a written analysis, explain what your conclusion is and why

Answer 1

Solution:

Here, we have to use one way analysis of variance or one way ANOVA F test for checking the given claim. The null and alternative hypotheses for this test are given as below:

Null hypothesis: H₀: There is a same amount of rainfall in every region in the Northwestern United States.

Alternative hypothesis; H_a: There is not the same amount of rainfall in every region in the Northwestern United States.

We are given

Level of significance = α = 0.02

The SPSS output for this test is given as below:

Descriptives
Rainfall
	N	Mean	Std. Deviation	Std. Error	95% Confidence Interval for Mean		Minimum	Maximum
					Lower Bound	Upper Bound
Plains	5	19.0000	3.57771	1.60000	14.5577	23.4423	16.50	25.20
Mountains	5	14.4200	2.60327	1.16422	11.1876	17.6524	11.30	18.10
Forest	5	14.5400	3.28070	1.46717	10.4665	18.6135	9.70	18.10
Total	15	15.9867	3.67907	.94993	13.9493	18.0241	9.70	25.20

ANOVA
Rainfall
	Sum of Squares	df	Mean Square	F	Sig.
Between Groups	68.137	2	34.069	3.369	.069
Within Groups	121.360	12	10.113
Total	189.497	14

The degrees of freedom for the test statistic F are given as 2 and 12.

The test statistic value for this test is given as F = 3.369.

The P-value for this test is given as 0.069.

P-value > α = 0.02

So, we do not reject the null hypothesis

There is insufficient evidence to conclude that there is not the same amount of rainfall in every region in the Northwestern United States with a significance level of 0.02.