Please follow the four steps of hypothesis testing to show your process of decision. t table is attached.

A researcher suspected that age is related to depression. It is known that the general population average m=40 on a standard depression test. The researcher obtained a sample of individuals (n=9) who are more than 75 years old. The depression score of this sample had M= 43, and s=3. On the basis of this sample, is depression for elderly people significantly different from depression in the general population at a=0.05 level?

Did the sample support researcher's hypothesis? Show the process for your decision.

Later, the researcher knew that the standard depression test has s=5 for population, would that change the conclusion? Show the process for your decision