Bergmann’s rule (named after German biologist Carl Bergmann) is an ecogeographical rule that states that within a species, specimens will tend to be larger if they are from cooler climates or more extreme latitudes. A Cal Poly biology graduate student investigated whether Bergmann’s rule applies to the golden mantled squirrel in California. She measured the body lengths (mm) of 18 squirrels from the following four California locations: Hemet (33.7° N), Big Bear Lake (34.2° N), Susanville (40.4° N), and Loop Hill (41.7° N). The summary statistics are shown in the following table, and the data are shown in the dotplots 

a. We want to determine whether there is strong evidence of an association between the location and the body length of the squirrels. State in words the null and alternative hypotheses for this test. 

b. Using the summary statistics given, compute the Mean Group Diff statistic. 

c. A null distribution for this study is shown below. Using the Mean Group Diff statistic you calculated in part (b), will the p-value for this test be large or small? Explain.

d. Does it appear there is strong evidence of an association between location and squirrel body length? If there is an association, can we conclude that location causes the difference? Explain  

Transcribed Image Text:

Location Loop Hill Susanville Big Bear Lake Hemet Sample size 4 Loop Hill Susanville Big Bear Lake Hemet 5 4 5 240 Standard Mean (mm) deviation (mm) 7.59 280.75 262.20 260.75 252.00 260 Length (mm) 280 10.89 10.75 7.97 300