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 19 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^3. An analysis of the sample data revealed that the hippocampal volume is approximately normal with x overbarxequals=8.11 cm cubedcm3 and

sequals=0.7 cm cubedcm3. Conduct the appropriate test at the alphaαequals=0.01 level of significance.

State the null and alternative hypotheses.

Upper H 0H0​: muμ __ __

Upper H 1H1​: muμ __ __

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

Identify the​ t-statistic.

t0= ​(Round to two decimal places as​ needed.)

Identify the​ P-value.

​P-valueequals= ​(Round to three decimal places as​ needed.)

Make a conclusion regarding the hypothesis.

_____ the null hypothesis. There ____

sufficient evidence to claim that the mean hippocampal volume is _______ _____ cm cubedcm3.

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is ,

H₀ :   = 9.02

H_a : < 9.02

Test statistic = t

= ( - ) / s / n

= (8.11 - 9.02) /0.7 / 19

= -5.67

df = 18

P-value = 0

= 0.01

P-value <

Reject the null hypothesis .

There is sufficient evidence to claim that the mean hippocampal volume is less than cm cubedcm3.