Question

Hello,

I want to measure the effect of alcohol on the hippocampal region, the portion of the brain responsible for long-term memory storage. I 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 cm3. An analysis of the sample data revealed that the hippocampal volume is approximately normal with X overbar = 8.05 cm3 and s= 0.8 cm3. I want to conduct the appropriate test at the a= 0.01 level of significance. What is the t-statistic and p-value?

Answer 1

Let denotes the mean normal volume.

To test against

Here

sample mean

sample standard deviation

and sample size

The test statistic can be written as

which under H₀ follows a t distribution with n-1 df.

We reject H₀ at 0.01 level of significance if p-value < 0.01

Now,

The value of the test statistic =

P-value =

Since p-value < 0.01, so we reject H₀ at 0.01 level of significance and we can conclude that the hippocampal volumes in the alcoholic adolescents were significantly less than the normal volume of 9.02 cm3.