Each of the following situations consists of two variables; for each situation, calculate the degrees of freedom ( \(d f\) ) and determine the critical value of \(\chi^{2}\) (assume \(\alpha=.05\) ).

a. Condition (Drug, Placebo) and Age (Young, Old)

b. Grade (Third, Sixth) and Score (Below Average, Average, Above Average)

c. Time of Day (Morning, Afternoon, Evening) and Activity (Running, Biking, Swimming)

d. Type of Car (Luxury, Sports, Sedan, Station Wagon) and Major (Business, Engineering, Social Sciences, Humanities)