“…Often scientists are able to provide information regarding the signs of various parameters under test and this information can be used to improve the power of testing procedures. Examples occur in statistics (BHATTI and KING (1990), EVANS and KING (1985), FAREBROTHER (1986), SENGUPTA (1987SENGUPTA ( , 1988, KING and EVANS (1986), WOLAK (1987)), econometrics (BHATTI (1991), HILLIER (1987), JUDGE and YANCEY (1986), KING and SMITH (1986), KING (1987a), KING and W u (1990), WU and BHATTI (1989)) and biometrics (BHATTI (1990), SOLOMON (1986, 1988)). This paper re-examines the problem considered by Cox and SOLOMON (1988) which involves testing for a non-zero autocorrelation coefficient, e, when one has a number of very small samples.…”