Question

Researchers wanted to measure the effect of alcohol on the development of a region of the brain (the hippocampus) responsible for long-term memory storage. The researchers randomly selected 12 adolescents with alcohol use disorders. They wanted to test the claim that hippocampal volumes in alcoholic teens were less than the normal volume of 9.02 centimeters cubed. An analysis of the sample data revealed that the volumes were approximately normal with a mean of 8.1 and standard deviation of 0.7. Test the claim at the 1% level of significance.

Answer 1

Step 1:

Ho: = 9.02

Ha: < 9.02

Null hypothesis states that the hippocampal volumes in alcoholic teens is equal to normal volume of 9.02 centimeters cubed

Alternative hypothesis states that the hippocampal volumes in alcoholic teens is less than normal volume of 9.02 centimeters cubed

Step 2: Test statistics

n = 12

sample mean = 8.1

sample sd = 0.7

Assuming that the data is normally distributed and also as the population sd is not given, we wil calculate t stat.

Step 3:

df = 11

= 0.01

t ciritcal (left tailed test) = - 2.718

As the t stat falls in the rejection area, we reject the Null hypothesis.

Hence we have sufficient evidence to believe that hippocampal volumes in alcoholic teens is less than normal volume of 9.02 centimeters cubed