Is a chi-square goodness of fit test always applied to a one way table?

Yes

Step-by-step explanation:

A chi-square test (y) examine whether it is good enough to fit, and associates a detected dispersal of Categorical data to the theorized dispersal shown in one-way table demonstrations distribution. If we get an empty hypothesis of the Chi test, it means no relationship exists between the categorial variables in the population, and they are not dependent on each other.

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.