1. At a big store building with 100 elevators, the amount of waiting time for next elevator in seconds is a Gaussian random variable (30,5) X. Suppose the significance level is a = 0.01 and null hypothesis H0 is that any event or occasion does not affect the probability distribution. Rejection set R is defined to be the set such that if the observation s is in R, then we reject the hypothesis H0.
(a) With a weekend sale going on, determine the rejection set R to 2 significant digits after decimal point (which is equal to {M100 (X) >= r1}, a one sided set and you have to compute r1. Hint: computed r1 is between 31 and 35).
(b) In a stormy day, determine the rejection set R (which is equal to {M100(X) <= r2 for a second value r2}.
(c) On the day with President's speech, determine the rejection set R (which is equal to {|M100(X) - 30| >= r3}, a two-sided set, for a third value r3).
(d) Explain why in parts (a), (b), (c) above, the rejection set R is one sided or two-sided.