High levels of cholesterol in the blood are not healthy in either humans or dogs

Question

High levels of cholesterol in the blood are not healthy in either humans or dogs. Because a diet rich in saturated fats raises the cholesterol level, it is plausible that dogs owned as pets have higher cholesterol levels than dogs owned by a veterinary research clinic. "Normal" levels of cholesterol based on the clinic's dogs would then be misleading. A clinic compared healthy dogs it owned with healthy pets brought to the clinic to be neutered. Here are the summary statistics for blood cholesterol levels (milligrams per deciliter of blood):

Group   n x s
Pets 25 186.02 74.89
Clinic 21 181.28 43.39

1) The standard error of the difference in sample means is_? (±0.0001).

2) Give a 90% confidence interval (±0.01) for the difference in mean cholesterol levels between pets and clinic dogs. Use the conservative degrees of freedom, and the pet dogs as group 1. _to_?

Explanation / Answer

1) For independnet small smaple size, compute standard error of difference of means for 2-sample t test.

SE(pets-clinic)=sqrt[sp^2/np+sc^2/nc]

=sqrt[74.89^2/25+43.39^2/21]

=17.72

2) The 90% c.i=(xpbar-xcbar)+-t39, 0.10 SE(pets-clinic)

=(186-181.3)+-1.6849*17.72

=-31.1 to 40.6

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