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 cm3. An analysis of the sample data revealed that the hippocampal volume is approximately normal with x̅ = 8.09 cm3 and s = 0.8 0.8 cm3. Conduct the appropriate test at the α = 0.01 level of significance.

State the null and alternative hypotheses.

H0​: μ

▼

greater than>

not equals≠

less than<

= __?__

H1​: μ

▼

greater than>

equals=

not equals≠

less than<

__?__

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

Identify the​ t-statistic.

t0=__?__

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

Identify the​ P-value.

​P-value=__?__

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

Make a conclusion regarding the hypothesis.

▼

Fail to reject

Reject

the null hypothesis. There

▼

is not

is

sufficient evidence to claim that the mean hippocampal volume is

▼

less than

greater than

equal to

__?__ cm3.

Answer 1

Solution :

Given that,

Population mean = = 9.02

Sample mean = = 8.09

Sample standard deviation = s = 0.8

Sample size = n = 13

Level of significance = = 0.01

This is a left tailed test.

The null and alternative hypothesis is,

Ho: 9.02

Ha: 9.02

The test statistics,

t = ( - )/ (s/)

= ( 8.09 - 9.02 ) / ( 0.8 / 13)

= -4.19

p-value = 0.001

The p-value is p = 0.001 < 0.01, it is concluded that the null hypothesis is rejected.

Conclusion:

Reject the null hypothesis, there is sufficient evidence to claim that the mean hippocampal volume is less than 9.08 cm³ ,at

0.01 level of significance.