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 alcohol adolescents were less than the normal volume of 9.02 cm3. An analysis of the sample data revealed that the hippocampal volume is approximately normal with x=8.06 cm3 and s=0.7 cm3.

Conduct the appropriate test at the a=0.01 level of signifcance.

State the null and alternative hypotheses

Ho:u (<, > , = , =/)______________

H1:(u >,<, =,==/)____________

(type integers or decimals. Do not round)

identify the t-statistic

to=____________________(Round to two decimals places as needed)

identify the P-value.

P-value=________________(round to three decimal places as needed)

Make a conclusion regarding the hypothesis.

Fail to reject or Reject the null hypothesis. There is or is not sufficient evidence to claim that the mean hippocampal volume is greater than, less than, or equal than cm3.

Answer 1

Null hypothesis     

           
                  
Alternative hypothesis      

           
                  
We have for given sample,                  
Population mean for given sample=9.02  
Sample mean=8.06          
Sample standard deviation s=0.7      
Sample size =n=   19          
                  
Degree of freedom = n-1 =18      
                  

                  
t test statistic formula is

P value is 0.0001 or approximately 0..................by using Excel command TDIST(-5.98,18,1)

P value is 0 < 0.01

Therefore, we reject H0.

Reject the null hypothesis. There is sufficient evidence to claim that the mean hippocampal volume is less than 9.02 cm3