[Continues from yesterday] Formally test the equality of the long-run average values for the indices at the two sampling stations, using a significance level of . Calculate the 95 percent confidence interval for the difference between the long-run averages. Explain the relationship between the results of these two statistical analyses.

In a study of the use of macroinvertebrate communities as pollution indicators, the effectiveness of a numerical species diversity index to indicate aquatic degradation due to acid mine drainage was investigated. A high diversity index should indicate an unstressed aquatic system. Two sampling stations were chose, one upstream and one downstream of the discharge point....Read More

A large dairy cooperative has three lines for packaging blocks of cheese. The packaging equipment is subject to random faults in that, on average, line A fails to stamp the sell-by date on label 1 in 200 times; the corresponding figures for lines B and C are 1 in 100 and 1 in 50. Of...Read More

Babies with a particular congenital disorder are born in a large maternity hospital at a rate of two per four-week accounting period (FWAP). In any given FWAP what is the probability that more than three babies with this condition will be born in the hospital?

A group of individuals contains ten people with blood group O, five with group A and five with group B. Give a formula for the probability that a random sample of size six will contain two people with each blood group.

An athlete conceals two performance enhancing tablets in a bottle containing eight vitamin tablets that are similar in appearance. If three tablets are selected at random for testing by drugs surveillance officials, what is the probability the cheating will be detected? You may assume that analysis is not error prone, i.e. if a performance enhancing...Read More

Locate the global maximum point on the curve .

Find the inflexion point on .

Prove that for all .

Prove that for all in .