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 13 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 overbarequals8.12 cm cubed and sequals0.8 cm cubed. Conduct the appropriate test at the alphaequals0.01 level of significance.

Answer 1

The hippocampus volumes in the alcoholic adolescents are less than the normal volume of 9.02 cm³

Explanation:

Let x= the hippocampus volumes in the alcoholic adolescents

We'll conduct a hypothesis test at the 0.01 significance level with

Null hypothesis: x = 9.02 cm³

Alternate hypothesis: x < 9.02 cm³

A sample of 13 alcoholic adolescents gives the parameters

size=N= 13

mean=M= 8.12 cm³

standard deviation= s= 0.8 cm³

According to the sample, with 99% confidence, t statistic for the value X=9.02 can be found using the formula:

t=
`(X-M)/((s)/(√(N) ) )` where

• M is the sample mean (8.12)
• s is the standard deviation of the sample (0.8)
• N is the sample size (13)

If we put these numbers in the formula:

t=
`(9.02-8.12)/((0.8)/(√(13) ) )` =4.056

One tailed critical value for the sample with 12 degrees of freedom (sample size-1) in 99% confidence level is 2.681.

Since t value (4.056) is bigger than the critical value, we fail to reject the alternate hypothesis, therefore reject the null hypothesis and accept alternate hypothesis.