3. The Municipal Transit Authority claims that, on weekdays, fewer passengers ride the train that departs at 8 a. m. than the one that departs at 2 p. m. The following sample statistics were determined. The table shows the average number of riders for each train, after samples from random days were taken for each train.
n s
Morning Train 30 323 41
Afternoon Train45 356 45
Test at the α=.05 level of significance whether the data provide sufficient evidence to conclude that fewerpassengers ride the morning.
a. State the Null and the Alternative Hypotheses, explaining which is which is and which is . (2)
c. State the conclusion about the claim and how you made the decision. (4)

Given: ad¯¯¯¯¯ is an altitude. prove: ab2+ac2=cb2 right triangle a b c with right angle a. point d lies on side b c and segment a d is drawn. angle a d c is a right angle. drag and drop a reason into each box to correctly complete the two-column proof. statement reason ad¯¯¯¯¯ is an altitude, and ∠bac is a right angle. given ∠adb and ∠adc are right angles. definition of altitude ∠bac≅∠bda ? ∠bac≅∠adc ? ∠b≅∠b ? ∠c≅∠c reflexive property of congruence △abc∼△dba ? △abc∼△dac aa similarity postulate abbd=cbab ? ab2=(cb)(bd) cross multiply and simplify. acdc=cbac polygon similarity postulate ac2=(cb)(dc) cross multiply and simplify. ab2+ac2=ab2+(cb)(dc) addition property of equality ab2+ac2=(cb)(bd)+(cb)(dc) substitution property of equality ab2+ac2=(cb)(bd+dc) ? bd+dc=cb segment addition postulate ab2+ac2=cb2 substitution property of equality