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 cubed. An analysis of the sample data revealed that the hippocampal volume is approximately normal with x overbarequals8.16 cm cubed and equals 0.7 cm cubed. Conduct the appropriate test at the alphaequals0.01 level of significance.

Answer 1

Answer:

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

Step-by-step explanation:

We are given the following in the question:  

Population mean, μ = 9.02

Sample mean, $\bar{x}$ = 8.16

Sample size, n = 23

Alpha, α = 0.01

Sample standard deviation, s = 0.7

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 9.02\text{ cm cubed}\\H_A: \mu < 9.02\text{ cm cubed}$

We use one-tailed t test to perform this hypothesis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{8.16 - 9.02}{\frac{0.7}{\sqrt{23}} } = -5.892$

Now,

$t_{critical} \text{ at 0.01 level of significance, 22 degree of freedom } = -2.508$

Since,                    

$t_{stat} < t_{critical}$

We fail to accept the null hypothesis and reject it. We accept the alternate hypothesis.

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