Explanations

1.) Many people have the common misconception that archaeologists study fossils and dinosaur activity.  However, this would be a broad defintion of the work of paleontologists, rather than archaeologists.

2.) While archaeologists use the other three choices, the most commonly used instrument by archaeologists is the trowel.  The trowel allows the user to srcrape away loose dirt when excavating sites, which is crucial to unearthing artifacts and features.  

3.) While finding artifacts is important, archaeologists are more concerned with understanding what the artifacts can tell about past human activity.  Archaeology is all about piecing together the past through the study of material culture left behind by past human civilizations.

4.) The belief of "archaeology as anthropology," (or "archaeology as science") started in the late 1950's in the U.S.  This way of thinking is known as "processual arhcaeology" and also commonly referred to as "new archaeology".  This theory was developed after criticism of the previous phase of archaeology known as the "culture-historical" phase.  Proponents of proccesual archaeology argued that the previous way of thinking was incorrect because it only focused on material culture to define diffrernt cultures or groups of people.  Proccesual archaeology advocates that cultural change is the result of a predictable framework due to environmental determinism.  Processual archaeology is also not without its criticism.  Since there is so much more to learn about this subject that is beyond the scope of this basic explanation, you can learn much more from these links:

Source of explanation above:

http://en.wikipedia.org/wiki/Processual_archaeology

Opposition to proccesual archaeology:

http://en.wikipedia.org/wiki/Post-processual_archaeology