Question

Consider the data below of inches of rainfall per month for three different regions in the
Northwestern United States:
Plains Mountains Forest
March 14.8 12.6 11.0
April. 21.4 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
September 16.9 16.7 14.2

Using SPSS, perform a two-sample t-test to test the hypothesis that there is not the
same amount of rainfall in both the Mountains and the Forest regions in the
Northwestern United States with a significance level of 0.02. You do not need to test
Normality first. In the output, the first test in the table (Levene’s Test for Equality of
Variances), concerns whether the variances of the populations are equal (the null
hypothesis) or not (the alternative hypothesis); we are assuming unequal variances in
this course, so use the second row. If parts of your table do not export, you can copy
and paste it to preserve the test statistic and significance from SPSS, or transcribe both
of them (and include what does export from the SPSS output). You should include the
hypotheses of your test, what the P-value is from the output, and your conclusion about
the hypotheses. What are the degrees of freedom of your test statistic (using the
formula from the book)?
Then, 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 0.03. You should include the hypotheses of your test, what the P-value is from
the output, and your conclusion about the hypotheses. What are the two degrees of
freedom of your test statistic?

Answer 1

The two-sample t-test SPSS Output is:

The hypothesis being tested is:

H₀: µ₁ = µ₂

H₁: µ₁ ≠ µ₂

The test statistic is 0.343.

The p-value is 0.738.

Since the p-value (0.738) is greater than the significance level (0.02), we fail to reject the null hypothesis.

Therefore, we cannot conclude that there is not the same amount of rainfall in both the Mountains and the Forest regions in the Northwestern United States.

The ANOVA test SPSS Output is:

The hypothesis being tested is:

H₀: µ₁ = µ₂

H₁: µ₁ ≠ µ₂

df1 = 1

df2 = 12

The test statistic is 0.118.

The p-value is 0.737.

Since the p-value (0.737) is greater than the significance level (0.03), we fail to reject the null hypothesis.

Therefore, we cannot conclude that there is not the same amount of rainfall in both the Mountains and the Forest regions in the Northwestern United States.