● What is it meant by the term “parameter of a population”? Explain why a population can be represented by a random variable.
● What is a point estimate, and an unbiased point estimate? Explain how the sample mean can be an unbiased estimate of the population mean. How do you justify that the sample variance is an unbiased estimate of the population variance? What is the sampling requirement in the latter case? Provide a numerical example of estimating the mean, the variance, and the standard deviation.
● Please define each of the following terms, discuss applicability and significance of each: sample statistic, standard error, sampling distribution, and central limit theorem. Include hypothetical examples for better clarity.
● What is the z statistic and what qualifies a statistic to be z statistic based on the central limit theorem and the basic properties of normal distributions? What are the limitations of the central limit theorem, and how some of these limitations are bypassed? For example, the z statistic as the sampling distribution in estimating a proportion.
● What is the sampling distribution in estimating the variance of a population? What are the properties of this distribution?
● What is the alternative of the z statistic for normally distributed populations which eliminates some limitations of the central limit theorem? How is this sampling distribution constructed as a combination of a z distribution and a chi squared distribution? What are the properties of this distribution?
Define each of the following terms and provide hypothetical example for each: hypothesis testing, null and alternative hypothesis, non-directional and directional hypothesis, type I error in testing hypothesis, type II error in testing hypothesis, probability of type I error (ɑ), probability of type II error (ß), power of the test and its significance, the critical value(s) in a test, p value (significance level).
● What is the difference between testing hypothesis on a population and testing hypothesis when comparing two populations? Provide hypothetical examples.
● What are the possible outcomes in testing a hypothesis? What are the determinant factors in deciding the critical value(s) in testing a hypothesis?
Event-related potentials (ERPs) are voltages generated by the brain due to sensory, motor, or cognitive stimuli. During ERPs, cortical pyramidal neurons fire action potentials as the brain is processing the stimuli. The summation of these postsynaptic potentials reflect the type of the ERP (Sur et al., 2009). For example, N1 waves is elicited when a auditory stimuli is presented (Sur et al., 2009). A P2 wave may be elicited in response to sensation seeking behavior (Sur et al., 2009). P3 waves may be elicited in response to unexpected target words (Sur et al., 2009). Studies have been conducted on patients in vegetative and minimally conscious states to investigate cortical functions by evaluating ERP responses to auditory cues. In a study done by Kotchoubey et al, all patients exhibited a ERP response, however the types of responses varied. Most patients displayed N1 and P2 waves while a third displayed P3 waves. Patients in the vegetative state were also found to have slightly lower ERP results compared to those of patients in the minimally conscious state (Kotchoubey et al., 2005). A study conducted by Perrin et al investigated semantic processing in patients in vegetative and minimally conscious states, by attempting to evoke ERPs using the auditory recordings of the patient’s name, revealed similar results. P3 waves were elicited in all minimally conscious patients and 60% of patients in a vegetative state (Perrin et al., 2006). Collectively, these studies imply that patients in vegetative and minimally conscious states have retained their auditory and language comprehension abilities. However, these results do not reflect consciousness, as ERPs can be generated in healthy unconscious patients as well.
GABA (gamma-Aminobutyric acid) is an inhibitory neurotransmitter and glutamate is a excitatory neurotransmitter. Both modulate activity and communication between neurons (Pontes et al., 2013). After brain injuries, a surge of GABA and glutamate enter the brain. The presence of glutamate results in the ischemic microenvironment becoming stabilized as apoptotic brain cells absorb toxic metabolites (Clauss, 2010). However, the inhibition caused by GABA begins to dominate, causing a suppression of cell metabolism to protect the cells. Brain functions are gradually suppressed as well, which results in a loss of consciousness. Subsequently, GABA starts to flow from the brain to the blood and the brain becomes depleted of GABA (Clauss, 2010). GABA receptors may then become over sensitive to the presence of GABA