Question

Healthy	AOAUD
10.82	9.32
10.71	8.73
10.56	8.46
10.49	8.46
10.30	8.42
9.49	8.23
9.32	8.12
9.25	8.09
9.20	7.97
9.08	7.82
9.06	7.05
9.02	6.63
8.98
8.77
8.77
8.72
8.60
8.45
8.40
8.04
7.92
7.93
7.87
6.47

1. Assume that the mean adjusted hippocampal volume for healthy adolescents is 9.01 cubic centimeters. State the hypotheses to test whether the AOAUD mean hippocampal volume is less than this value.

To perform the hypothesis test, we will compute H₀: m = 9.01 and H_A: m < 9.01. By doing this, we get the results:

Hypothesis test results:

Variable	Sample Mean	Std. Err.	DF	T-Stat	P-value
var1	9.0091667	0.21260711	23	-0.003919593	0.4985

2. Compute the t-value and the P-value for this test.

?

Answer 1

(1) We have to test whether the mean adjusted hippocampal volume for healthy adolescents is less than 9.01 cubic cm, so this statement will be out alternate hypothesis statement.

Null hypothesis (Mean adjusted hippocampal volume for healthy adolescents is equal to 9.01 cubic cm)

Alternate hypothesis (Mean adjusted hippocampal volume for healthy adolescents is less than 9.01 cubic cm)

(2) Data table provided in the question shows us the calculated t value and its corresponding p value.

t calculated = -0.00392 and the p value is 0.4985

At 0.05 significance level, the p value corresponding to the calculated t statistic is insignificant because the p value is greater than 0.05 significance level.

So, we failed to reject the null hypothesis and thus we can conclude that we have insufficient evidence to claim that the mean adjusted hippocampal volume for healthy adolescents is less than 9.01 cubic cm