Could you please explain these questions and definitions? a. why variability is important to measure, and what higher variability does to your chances ofsignificance and your overall confidence in your resultb. relationship between power and sample sizec. how things like variability, sample size, and effect size effect the size of obtained t-scores andF ratiosd. the difference between positive and negative correlation, the difference between correlationand causatione. the difference between type I and type II errors and how we either measure the risk of orcontrol for these errors (HINT: your alpha is important for one of these, power for the other)f. what sampling error is and what it has to do with hypothesis testingg. general terminology like "null hypothesis," "alternative hypothesis," "independent variable,"etc.

Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts for you. To get the remaining sub-part solved please repost the complete question and mention the sub-parts to be solved. a. Variability is a measure of spread or dispersion. It tells us the spread of each data point in a data distribution from its center. Variability expresses the spread of observations in terms of the distance between the values of selected observations. The three measures of variabilities are: Variance/ standard deviation. Range. Interquartile range. The variability tells us about the spread of the data distribution which helps in generalizing the results and also helps in comparing two data distributions with respect to their variability. Higher variability means the values are less reliable, so it's difficult to make predictions. Higher variability minimizes the ability to detect the statistical significance that can make predictions difficult about the population based on the sample data.b. Relationship between Power and sample size: The relationship between sample size and power is described in such a way that as the sample size gets increases, reduces the value of standard error by increasing the power. The sample size can be obtained as: n=zα/2+zβ∆2 where, α=Significance level ( confidence level ,1-α)1-β=Power or equivalently, type II error rate β ∆=μ1-μ0σc. how things like variability, sample size, and effect size affect the size of obtained t-scores and F ratios: The t-test statistic formula is given as: t=x¯-μs2/n The larger the variance of a sample, the less likely the t statistic will be significant, and the smaller the effect size will be. When we have a larger sample size, the standard error will be smaller the statistic is more likely to be significant. The denominator of the F-ratio will change as the sample variance increases.d. The difference between positive and negative correlation, the difference between correlation and causation Positive Correlation Negative Correlation If the two variables move in the same direction consistently then there is a positive correlation. If the two variables move in opposite directions then there is a negative correlation. When one variable increases, the other variable also increases, and when one variable decreases, the other variable also decreases. When one variable increases, the other variable decreases, and vice versa. Correlation analysis is used to measure the strength of the association between variables. The association or relationship between the variables is said to be strong if all the points are close to a straight line. It is said to be weak if all points are far away from the straight line and it is said to be moderate if the data points are moderately close to a straight line. Causation: If one event appears or causes because of the occurrence of another event then the two events are said to have a casual relationship. Reference: https://naldc.nal.usda.gov/download/IND43966364/pdf