9. In a study, researchers wanted to measure the effect of alcohol on the hippoc

Question

9. 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 18 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= 8.02 cm3 and s= 0.8 cm3. Conduct the appropriate test at the a= 0.01 level of significance.

State the null and alternative hypotheses.

Select;

greater than>

equals=

less than<

not equals

H0: u __?___ ___?___ (Type integers or decimals. Do not round.)

H1 : u __?__ ___?___ (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.

(1) Fail to reject or reject

(2) is or is not

(3) equal to, greater than, or less than

_____(1)__?_ the null hypothesis. There __(2)__?_ Sufficient evidence to claim that the mean hippocampal volume is ___(3)__?__   __?__ cm3

Explanation / Answer

Below are the null and alternate hypothesis
H0: mu = 9.02
H1: mu < 9.02

Test statistics,
t0 = (8.02 - 9.02)/(0.8/sqrt(18))
t0 = -5.3033

p-value = 0.0000

As p-value is less than the significance level of 0.01, we reject the null hypothesis

there is sufficient evidence to claim that the mean hippocampal volume is less than 9.02

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