5. A number of studies have related the size of the hippocampus, the brain region involved in memory and stress, to the risk of developing post-traumatic stress disorder (PTSD). Previous studies have indicated that individuals with small hippocampi are more likely to develop chronic forms of stress disorder. The hippocampi of 16 veterans of the Gulf War who were suffering from PTSD were measured using magnetic resonance imaging. The data are presented below as volumes in cubic centimeters. 1.4 1.5 1.4 1.7 1.4 1.3 1.8 1.3 2.0 1.5 1.4 1.2 1.1 1.7 1.4 1.9 If the average size for the hippocampus in the general population is 1.8 cm3, do the above data support the conclusions of the earlier studies? Assume volumes are normally distributed. x= 1.5 cm, s = 0.25 cm Conduct a hypothesis test by doing the following: a. Write out the hypotheses (H and HA) associated with the scientific question. | b. What is the null value, H., in the hypotheses? c. Find the p-value, by using R to compute the exact p-value (attach R code and output). I d. Provide the meaning/iterpretation of this p-value to draw a conclusion about the hypotheses in (a) and answer the scientific question. e. State the type I and type II errors in the context of this study. f. Which type of error (I or II) could be committed in this hypothesis test?