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For a statistics assignment, I have two different questions involving testing hypotheses.

The first question concerns flu shots and whether or not patients had flu or no flu. So we have two categorical response variables(flu or no flu) and three categorical explanatory variables(no flu shot, one flu shot, two flu shots). I'm assuming use a chi squared test?

The second question involves peak expiratory flow between two different groups of children given two different medications. It asks to provide the most appropiate graph to compare the distribution, and also to carry out the appropriate hypothesis test. For comparing two different sets of data, both with a continuous response variable and a categorical explanatory variable, which would be the best hypothesis test?

Thanks in advance for any help.