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 11 adolescents with alcohol use disorders to determine whether the hippocampal volumes in the alcoholic adolescents were less than the normal volume of 9.02cm^3. An analysis of the sample data revealed that the hippocampal volume is approximately normal with no outliers and x overbarxequals=8.18cm^3 and sequals=0.7cm ^3. Conduct the appropriate test at the alphaαequals=0.01 level of significance. State the null and alternative hypotheses. Upper H 0​: mu ▼ greater than less than not equals nothing Upper H 1​: mu ▼ greater than not equals less than nothing ​(Type integers or decimals. Do not​round.) Identify the​ t-statistic. t 0equalsnothing ​(Round to two decimal places as​ needed.) Identify the​ P-value.​P-valueequalsnothing ​(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 ▼ greater than less than equal to nothing cm cubed. Enter your answer in each of the answer boxes.

Answer 1

Solution :

= 9.02

= 8.18

s = 0.7

n = 11

Df = n-1 = 11-1 = 10

This is the left  tailed test .

The null and alternative hypothesis is

H0 :   = 9.02

Ha : < 9.02  

Test statistic = t

= ( - ) / s / n

= ( 8.18 -9.02) / 0.7 / 11

= -3.98

p(Z > -3.98 ) = 1-P (Z < -3.98) =0.003

P-value = 0.003

= 0.01

0.003 < 0.01

Fail to reject Reject the null hypothesis.

There is not is sufficient evidence to claim that the mean hippocampal volume is 9.02cm^3 less than equal to nothing cm cubed.