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 22 adolescents with alcohol use disorders to determine whether the hippocampal volumes in the alcoholic adolescents were less than the normal volume of 9.02cm3. An analysis of the sample data revealed that the hippocampal volume is approximately normal with

x overbarxequals=8.06cm3 and s=0.7cm3. Conduct the appropriate test at the α=0.01 level of significance.

(a) State the null and alternative hypothese

(b) Identify the t- statistic and p value

(c) Conclusion: (reject/Fail to reject) __ the null hypothesis. There (is/is not) __ sufficent evidence to claim that the mean hippocampal volume is (equal to/less than/greater than) __ __ cm3

Answer 1

Since we are comparing one sample mean (mean hippocampal volume) with the population and the population standard deviation is not known, the t-test for One Population Mean is be used.

a)

The Null and Alternative Hypotheses

Since the researcher wants to test the claim that alcohol effect the hippocampal​ region (reduce)

b)

The t statistic is obtained using the formula,

Where,

Sample average = 8.06

Sample standard deviation = 0.7

Sample size = 22

The t-statistic is,

The p-value is obtained from t distribution table for degree of freedom = n - 1 = 22 - 1 = 21 and t-statistic = -6.4326

c)

Answer:  Reject the null hypothesis. There is sufficient evidence to claim that the mean hippocampal volume is less than 9.02 cm3

Explanation:

Since the P-value is less than significance level = 0.01 hence, it can be concluded that the null hypothesis is rejected.