If a researcher studies fourth-grade students to determine the effects of rewarding

student grade level

Explanation:

The case of the extraneous variable is most likely to be determined by the student grade level that is level of the education program that is for the grade level. This refers to all the course level and can be use to trace out the external variable that are not intentionally studied in the test or experiment and tends to affect the other variables.

Dr. Winkle is most likely a developmental psychologist.

Explanation:

Developmental psychology is a field that studies the various changes that occur in the humans during their life. It involves examining the changes in human beings of all age groups. It studies the cognitive, socioemotional and physical development of the human beings which include personality, identity information, language, motor skills, moral understanding, emotional development, etc.  

Therefore, Dr. Winkle is most likely a developmental psychologist.