What assumption can be made if a twin-study design project reveals that the correlation between identical twins on a given trait is substantially higher than that between fraternal twins?

Several assumptions can be made using these results. The one of the main assumption is that these result prove the higher similarity among identical twins then of those who are fraternal. This is because the identical twins share mostly same amount of genome from both parents as a single zygote that is fertilized by one sperm divides into two. On the other hand, all fraternal are dizygotic. It means that there were two eggs that were fertilized by two totally different sperms. They do not share any of characteristics but may share some with parents.  

The answer is Sickle cell anemia. It is a condition that results in the formation of the abnormal hemoglobin. It is an inherited form in which the healthy red blood cells cannot carry enough oxygen all throughout one's body then.