Question

In a​ study, researchers wanted to measure the effect of alcohol on the hippocampal​ region, the portion of the brain responsible for​ long-term memory​ storage, in adolescents. The researchers randomly selected 14 adolescents with alcohol use disorders to determine whether the hippocampal volumes in the alcoholic adolescents were less than the normal volume of 9.02 cm cubed. An analysis of the sample data revealed that the hippocampal volume is approximately normal with x overbarequals 8.05 cm cubed and s=0.7 cm cubed. Conduct the appropriate test at the alpha =0.01 level of significance.

Identify the​ t-statistic.

Answer 1

H0: = 9.02

H1: < 9.02

Standard error = s / = 0.7 / = 0.1871

Test Statistic, t = (x - ) / Std error

= (8.05 - 9.02) / 0.1871

= -5.18

Degree of freedom = n - 1 = 14 - 1 = 13

P-value = P(t < -5.18) = 0.00009

Since p-value is less than 0.01 significance level, we reject null hypothesis H0 and conclude that there is significant evidence that < 9.02 and hippocampal volumes in the alcoholic adolescents were less than the normal volume of 9.02 cm.