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 23 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 no outliers and x=8.16 cm3 and s=0.7 cm3. Conduct the appropriate test at the α=0.01 level of significance.

Answer 1

We do not reject the Null Hypothesis

Explanation:

From the question we are told that:

Sample size
`n=23`

Population mean
`\mu=9.02cm^3`

Sample mean
`\=x=8.16`

Standard deviation
`\sigma=0.7cm^3`

Significance level
`\alpha =0.01`

Generally the Null and and alternative Hypothesis are as follows

`H_0:\mu=9.02cm^3`

`H_a:\mu<9.02cm^3`

Therefore t critical Value is

`t\ critical\ Value=(\alpha,df)`

`t\ critical\ Value=(0.01,22)`

Where

`df=n-1\\\\df=23-1=>22`

Therefore

From t Table

`t value=-2.8`

Generally the equation for Z Critical is mathematically given by

`t=(\=x-\mu)/((\sigma)/(√(n) ) )`

`t=(8.16-9.02)/((0.7)/(√(23) ) )`

`t=-5.89`

Therefore

Since the t test statistics is greater than the Critical value

Hence,we do not reject the Null Hypothesis