The statement that if the distance between a light source and an observer is doubled, the intensity of
the light decreases by a factor of four, describes a consistent, repeatable observation that has been
confirmed through numerous experiments. This describes a scientific law, specifically the inverse
square law of light. A law summarizes a pattern found in nature, whereas a hypothesis is an untested
prediction, a theory is a well-substantiated explanation, and an inference is a conclusion drawn from
evidence. Reference:
Integrated Physical Sciences, Chapter 4: Scientific Laws and Theories

An appropriate question for an observational study is one that involves collecting data through
observation without manipulation. "What types of rocks are found at a convergent boundary?"
requires observing and identifying the types of rocks naturally occurring at such geological
formations. It doesn't involve changing any variables, fitting the definition of an observational study.
Reference:
Integrated Physical Sciences, Chapter 2: Methods of Scientific Investigation

The scientist is determining how the speed of flowing water affects the size of sediment particles it
can carry by varying the water speed and measuring the sediment sizes. This involves manipulating
one variable (water speed) and observing the effect on another variable (sediment size), which is the
essence of a controlled experiment. The setting and control of conditions ensure that the
experimenter can establish a cause-and-effect relationship.

Reference:
Integrated Physical Sciences, Chapter 2: Methods of Scientific Investigation

An observational study involves collecting data without manipulating any variables. The question
"What is the brightest star that can be seen from Earth?" fits this criteria as it involves observing and
recording data about stars without any experimental intervention. Other options involve controlled
experiments where variables are manipulated.

Reference:
Integrated Physical Sciences, Chapter 2: Methods of Scientific Investigation