Question

Consider the data below of inches of rainfall per month for three different regions in the Northwestern United States: Plains Mountains Forest

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? Please attach your Word file and, in a written analysis, give your answers and explain your conclusions by Sunday, July 26th at midnight Eastern Time

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.

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