Question

A study was conducted to find out if eating whole-wheat products was associated with a reduction
in body mass index (BMI) in adults. Researchers randomly assigned participants into two groups
(eaters and non-eaters of whole-eat products) for a two-month period. The average BMI reduction
for the 155 adults who ate whole-wheat products was 2.3 and the standard deviation was 1.1.
For the 148 adults who did not eat whole-wheat products the average BMI reduction was 1.2 and
the standard deviation was 0.8. Considering a level of significance of 0.05 (5%), build a test of
hypotheses to assess whether the average reduction in BMI would be different between eaters and
non-eaters of whole-wheat products for the population of adults similar to the ones in this study.
a) Is this a one-sided or a two-sided test? Why?
b) Specify all four steps of your hypothesis test. Show all calculation detail

Answer 1

Let denote average reduction in BMI for adults who ate whole-wheat products and for adults who did not eat whole-wheat products respectively.

a) and b)