22. Regional daily demand for gasoline in the summer driving months is assumed to be the outcome of a N(m, s2

)

random variable. Assume you have 40 iid daily observations on daily demand for gasoline with quantity demanded measured in millions of gallons, and x ¼ 43 and s2 ¼ 2.

(a) Show that N(m,s2

) is a location-scale parameter family of PDFs (recall Theorem 10.13).

(b) Define a pivotal quantity for m, and use it to define a

.95 level confidence interval for m. Also, define a .95 lower confidence bound for m.

(c) Define a pivotal quantity for s2

, and use it to define a

.95 level confidence interval for s2

.

(d) A colleague claims that mean daily gasoline demand is only 37 million gallons. Is your answer to

(b) consistent with this claim? Explain.