Chapter 9.2, Problem 17Q

A person exposed to an infectious agent, either by contact or by vaccination, normally develops antibodies to that agent. Presumably, the severity of an infection is related to the number of antibodies produced. The degree of antibody response is indicated by saying that the person’s blood serum has a certain titer, with higher titers indicating greater concentrations of antibodies. The following table gives the titers of twenty-two persons involved in a tularemia epidemic in Vermont $\left(21\right)$. Eleven were quite ill; the other eleven were asymptomatic. Use Theorem 9.2.3 to test $H_0:{\mu }_X={\mu }_Y$ against a one-sided $H_1$ at the 0.05 level of significance.

The sample standard deviations for the “Severely Ill” and “Asymptomatic” groups are 428 and 183, respectively.

Severely III		Asymptomatic
Subject	Titer	Subject	Titer
1	640	12	10
2	80	13	320
3	1280	14	320
4	160	15	320
5	640	16	320
6	640	17	80
7	1280	18	160
8	640	19	10
9	160	20	640
10	320	21	160
11	160	22	320