Researchers wanted to measure the effect of alcohol on the development of the hi

Question

Researchers wanted to measure the effect of alcohol on the development of the hippocampal region in adolescents. The researchers randomly selected 14 adolescents with alcohol use disorders. They wanted to determine whether the hippocampal volumes in the alcoholic adolescents were less than the normal volume of 9.02 cm cubed3. An analysis of the sample data revealed that the hippocampal volume is approximately normal with x=8.09 and s=0.8. Conduct an appropriate test at the a= 0.05 level of significance.
Researchers wanted to measure the effect of alcohol on the development of the hippocampal region in adolescents. The researchers randomly selected 14 adolescents with alcohol use disorders. They wanted to determine whether the hippocampal volumes in the alcoholic adolescents were less than the normal volume of 9.02 cm cubed3. An analysis of the sample data revealed that the hippocampal volume is approximately normal with x=8.09 and s=0.8. Conduct an appropriate test at the a= 0.05 level of significance.

Explanation / Answer

Given that,
population mean(u)=9.02
sample mean, x =8.09
standard deviation, s =0.8
number (n)=14
null, Ho: =9.02
alternate, H1: <9.02
level of significance, = 0.05
from standard normal table,left tailed t /2 =1.771
since our test is left-tailed
reject Ho, if to < -1.771
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =8.09-9.02/(0.8/sqrt(14))
to =-4.3497
| to | =4.3497
critical value
the value of |t | with n-1 = 13 d.f is 1.771
we got |to| =4.3497 & | t | =1.771
make decision
hence value of | to | > | t | and here we reject Ho
p-value :left tail - Ha : ( p < -4.3497 ) = 0.00039
hence value of p0.05 > 0.00039,here we reject Ho
ANSWERS
---------------
null, Ho: =9.02
alternate, H1: <9.02
test statistic: -4.3497
critical value: -1.771
decision: reject Ho
p-value: 0.00039

hippocampal volumes in the alcoholic adolescents were less than the normal volume

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