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 cm3. An analysis of the sample data revealed that the hippocampal volume is approximately normal with x overbar x equals = 8.13 cm cubed cm3 and s = 0.7 cm cubed cm3. Conduct the appropriate test at the alpha α equals = 0.01 level of significance.

Whats the T0?

(round to two decimals as needed)

Answer 1

Solution :

Given that,

Population mean = $\mu$ = 9.02

Sample mean = $\bar x$ = 8.13

Sample standard deviation = s = 0.7

Sample size = n = 23

Level of significance = $\alpha$ = 0.01

This is a left tailed test.

The null and alternative hypothesis is,

Ho: $\mu$ $\geq$ 9.02

Ha: $\mu$ 9.02

The test statistics,

t₀ = ( $\bar x$ - $\mu$ )/ (s/$\sqrt{n}$)

= ( 8.13 - 9.02) / ( 0.7 / $\sqrt{}$ 23)

= -6.10

p-value = 0

The p-value is p = 0 < 0.01, it is concluded that the null hypothesis is rejected.

Conclusion:

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the hippocampal

volumes in the alcoholic adolescents were less than the normal volume of 9.02, at the 0.01 significance level.