As the world warms, the geographic ranges of species might shift toward cooler a

Question

As the world warms, the geographic ranges of species might shift toward cooler areas. Chen et al. (2011) studied recent changes in the highest elevation at which species occur. Typically, higher elevations are cooler than lower elevations. Below are the changes in highest elevation for 20 of the 31 taxa examined in this study, in meters, over the late 1900s and early 2000s. (Taxa included plants, vertebrates, and arthropods.) Positive numbers indicate upward shifts in elevation, and negative numbers indicate shifts to lower elevations. The values are also displayed in the attached graph. How many degrees of freedom will be associated with a confidence interval and a one-sample t-test for the mean elevational range shift in these 20 species?

58.9 7.8 108.6 44.8 19.2 30.5 7.4 39.3 24 62.1 24.3 32.7 65.3 -19.3 -5.2 -2.1 31 88.6 20.7 89

Elevation change in m 8 6 4 0 I-19.3, 0.7] (0.7, 20.7] (20.7, 40.7] (40.7, 60.7] (60.7, 80.7] (80.7, 100.7100.7, 120.7]

Explanation / Answer

One sample t-test (One-tailed):

Ho: Mean elevational range shift is not positive OR x<=0

H1: Mean elevational range shift is positive OR x>0

We can use the following formula:

x = 36.38 (Mean), u = 0

s = 33.78, n = 20

t = 4.81

Degrees of freedom associated (Numer of scores that are free to vary) = N - 1 (N is the sample size)

df = 20 - 1 = 19

Hence, t-critical value at df = 19 and Alpha = 0.05 is 1.833

As t>tc, we can reject the null hypothesis and conclude that mean elevational range is positive.

Formula to calculcate confidence interval:

Hence, interval: (36.38 - 1.833*33.78/ sqrt(20), 36.38 + 1.833*33.78/ sqrt(20))

CI: (22.53,50.22)

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