Question

Please walk me through SPSS to answer this question...

Consider the data below of inches of rainfall per month for two different regions in the Northwestern United States:

Plains Mountains

April 25.2 13.0

May 17.1 18.1

June 18.9 15.7

July 17.3 11.3

August 16.5 14.0

Using SPSS, perform a two-sample t-test for the hypothesis that there is not the same amount of rainfall in both regions in the Northwestern United States with a significance level of 0.025. What are the degrees of freedom of your test statistic?

Answer 1

Solution:

Here, we have to use two sample t test for the difference between two population means.

Null hypothesis: H₀: There is no significant difference in the amount of rainfall in both regions in the Northwestern United States.

Alternative hypothesis: H_a: There is a significant difference in the amount of rainfall in both regions in the Northwestern United States.

H₀: µ₁ = µ₂ versus H_a: µ₁ ≠ µ₂

We are given

Level of significance = α = 0.025

The required SPSS output for this test is given as below:

Group Statistics
	Area	N	Mean	Std. Deviation	Std. Error Mean
Rainfall	Plains	5	19.0000	3.57771	1.60000
	Mountains	5	14.4200	2.60327	1.16422

Independent Samples Test
		Levene's Test for Equality of Variances		t-test for Equality of Means
		F	Sig.	t	df	Sig. (2-tailed)	Mean Difference	Std. Error Difference	95% Confidence Interval of the Difference
									Lower	Upper
Rainfall	Equal variances assumed	.177	.685	2.315	8	.049	4.58000	1.97874	.01702	9.14298
	Equal variances not assumed			2.315	7.308	.052	4.58000	1.97874	-.05926	9.21926

For this test, the test statistic value is given as t = 2.315.

The degrees of freedom is given as df = 8.

The P-value is given as 0.049.

P-value > α = 0.025

So, we do not reject the null hypothesis

There is insufficient evidence to conclude that there is not the same amount of rainfall in both regions in the Northwestern United States with a significance level of 0.025.