souree documents Ralph manages a consulting companyand is presently looking over the time sheets for the last 12 engagements, wond~ring how mueh staff time is involved in a typical engagement. Ralph decides to think of this as a population that is Normally distributed with unknown mean,u and unknown varianee cJl. So if xj is the total staff time required on engagement j, Ralph regards xj as a draw from a Normal distribution with mean,u and variance cJl. Using the noted data and a handy statistics paekage, Ralph estimates the mean (142 hours) and standard deviation (29 hours).

A confidence intelVal estimate of the mean is also provided, relying on the faet a random sample from a Normal population leads to aStudent t distribution.

The times on the time sheets are reported by the staff themselves. Ralph also knows that, if the firm is particularly busy, the staff will work overtime to complete their assignments and will not report the extra hours.

a] Is Ralph' s sample mean a biased estimator of the population mean? Carefully but thoroughly explain your answer.

b] Is Ralph's estimate of the population varianee (or standard deviation) a biased estimator? Again, earefully but thoroughly explain your answer.

e] What additional statistieal exploration might Ralph engage to eonfirm or allay these fears?

d] What prineiple of internai control is violated by this story?AppendixLO1