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

23

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 cubedcm3.

An analysis of the sample data revealed that the hippocampal volume is approximately normal with no outliers and

x overbarxequals=8.12

cm cubedcm3

and

sequals=0.8

cm cubedcm3.

Conduct the appropriate test at the

alphaαequals=0.01

level of significance.

State the null and alternative hypotheses.

a). State the null and alternative hypotheses.

b). Identify the t-statistic.

c). Identify the P-value.

d). Make a conclusion

Answer 1

The provided information is:

-The sample mean is 8.12 cm³.

-The standard deviation of the sample (s) is 0.8 cm³.

-The sample size (n) is 23.

-The significance level is 0.01.

-The researcher wants to check that the hippocampal volumes in the alcoholic adolescents were less than the normal volume of 9.02 cm³.

(a):

The null and the alternative hypothesis is,

  

It is a left-sided test.

(b):

The test statistic is given as,

  

Thus, the test statistic is -5.395.

(c):

The degrees of freedom, df = n – 1 = 23 – 1 = 22

The p-value obtained at the test statistic (-5.395) and the degrees of freedom (22) from the t-table is,

P(T<t) = P(T<-5.395) = 0.00001

Therefore, the p-value is 0.00001.

(d):

Since the p-value (0.00001) is less than the significance level 0.01, so the researcher rejects the null hypothesis. Hence the result is statistically significant.

Therefore, the researcher concluded that there is sufficient evidence to support that the hippocampal volumes in the alcoholic adolescents were less than the normal volume of 9.02 cm³.