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 19 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 no outliers and x overbar equals 8.14 cm cubed and sequals 0.7 cm cubed. Conduct the appropriate test at the alpha equals 0.01 level of significance.

Answer 1

Answer:

n=19,  = 9.02, = 8.14, s= 0.7, = 0.01

null and alternative hypothesis is

Ho:    = 9.02

Ha:    < 9.02

formula for test statistics is

t = -5.48

test statistics= -5.48

calculate P-Value for left tailed test with df= n-1 = 19-1 = 18

using t table we get

P-Value = 0

decision rule is

Reject Ho if ( P-Value ) < ( )

here, ( P-Value= 0 ) < ( = 0.01 )

Hence, we can say,

Null hypothesis is rejected.

Reject the null hypothesis. There is sufficient evidence to claim that the mean hippocampal volume is less than 9.02 cm cubedcm3.