Suppose you study the differences between African elephants

Suppose you study the differences between African elephants (Loxodonta africana) and Asian
elephants (Elephas maximus) and want to see if African elephants can lift significantly more
weight with their trunks than Asian elephants. You collected data from adult females of both species, with the following results:

   Maximum Trunk Lift Weight (kg)
Species n Ybar s

African 33 345 27

Asian 29 329 12

a. If you are able to meet all assumptions of a t test except the assumption of equal
variances for the two populations of weights, which test should you use to analyze this data? (1pt)

b. Run this test and include all steps for full credit, given that df = 59 and using a 1%
significance level. (You do not need to check assumptions.) (4pt)

Solution

A)

We should use the 2-sample unpooled t test.

b)

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   <=   0  
Ha:   u1 - u2   >   0  
At level of significance =    0.01          
As we can see, this is a    right   tailed test.      
Calculating the means of each group,              
              
X1 =    345          
X2 =    329          
              
Calculating the standard deviations of each group,              
              
s1 =    27          
s2 =    12          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    33          
n2 = sample size of group 2 =    29          
df =    59          
Also, sD =    5.201579215          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    3.075988914          
              
where uD = hypothesized difference =    0          
              
Now, the critical value for t is              
              
tcrit =        2.390119473      
              
Thus, comparing t > 2.39012, we decide to   WE REJECT THE NULL HYPOTHESIS.          
              
Thus, there is significant evidence that African elephants can lift significantly more
weight with their trunks than Asian elephants. [CONCLUSION]