Question

Researchers wanted to measure the effect of alcohol on the development of the hippocampal region in adolescents. The researchers randomly selected 11 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 cubed cm3. An analysis of the sample data revealed that the hippocampal volume is approximately normal with x (overbar) = 8.32 and s = 0.8. Conduct an appropriate test at the ? = 0.05 level of significance. Show the correct hypothesis. Find the test statistic and the p-value. What conclusion can be drawn?

Answer 1

H₀: = 9.02

H₁: < 9.02

The test statistic t = ()/(s/)

                             = (8.32 - 9.02)/(0.8/sqrt(11))

                             = -2.90

DF = 11 - 1 = 10

P-value = P(T < -2.90)

             = 0.0079

As the P-value is less than significance level (0.0079 < 0.05), so we should reject the null hypothesis.

So we can conclude that the hippocampal volumes in the alcoholic adolescents were less than the normal volume of 9.02cm cubed.