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

1818

adolescents with alcohol use disorders to determine whether the hippocampal volumes in the alcoholic adolescents were less than the normal volume of

9.029.02

cm cubedcm3.

An analysis of the sample data revealed that the hippocampal volume is approximately normal with

x overbarxequals=8.078.07

cm cubedcm3

and

sequals=0.80.8

cm cubedcm3.

Conduct the appropriate test at the

alphaαequals=0.010.01

level of significance.

State the null and alternative hypotheses.

Upper H 0H0​:

muμ

▼

less than<

not equals≠

greater than>

equals=

nothing

Upper H 1H1​:

muμ

▼

equals=

less than<

greater than>

not equals≠

nothing

​(Type integers or decimals. Do not​ round.)

Identify the​ t-statistic.

t 0t0equals=nothing

​(Round to two decimal places as​ needed.)

Identify the​ P-value.

​P-valueequals=nothing

​(Round to three decimal places as​ needed.)

Make a conclusion regarding the hypothesis.

▼

Reject

Fail to reject

the null hypothesis. There

▼

is

is not

sufficient evidence to claim that the mean hippocampal volume is

▼

greater than

less than

equal to

nothing

cm cubedcm3.

Answer 1

The null and the alternative hypothesis-

i.e., the true mean hippocampal volume(cm³) in alcoholic adolescents is not different than that of normal volume of 9.029cm³ .

i.e., the true mean hippocampal volume(cm³) in alcoholic adolescents is less than the normal volume of 9.029cm³ .

To test this hypothesis at the researcher randomly selected the adolescents with alcohol use disorders, and the sample mean and standard deviation is calculated as,

Test-statistic:

; with degrees of freedom, df=n-1

The test-statistic is calculated as

P-value: Since it is a left-tailed hypothesis , so the p-value for the test-statistic of with degrees of freedom, df=n-1=18-1=17, is calculated to be as-

Conclusion:

Since,

At the does provide sufficient evidence to support the alternative hypothesis, and to reject the null hypothesis, H₀ .

In other words, we can conclude that we have sufficient evidence to believe that the alcoholic adolescents have the hippocampal volume less than the normal volume of 9.029cm³.