Question 1
Critical value method involves determining the likeliness or unlikeliness by determining whether the test statistic observed is more extreme than the null value or not. P-value is the probability of getting a value of sample test statistic that is far from the expected to be observed if null hypothesis holds true.
Question 2
F distribution is a ratio of two chi square random variables. The variance has a tendency to match the chi square distribution if one contains a normal random variable. It is used to determine if two variances are equal and to analyze variance and covariance figures. T distribution approximates the standard normal. The difference between f distribution and t distribution is that the f distribution assumes that you know the variance of the population while t distribution accounts for the uncertainty in measuring sample variance. F distribution determines which factors or interactions are significant in the model while the f distribution does not determine such factors. Unlike the t distribution, F distribution is symmetrical and only the positive values are taken into consideration.
Question 3
Concordant pair is a bivariate observation data-set {x1,y1} and {x2,y2} in which sgn(x2-x1) =sgn(y2-y2).
A discordant pair is a pair of two variables in which sgn(x2-x) = -sgn(y2-y1). Sgn is a sign function often defined by:
The McNemar’s test uses the 2 by 2 classification table when doing comparisons in different paired proportions. The McNemar’s test will use a concordant pair; the variables being numeric or alphanumeric.
Part 2
In this study the researcher wishes to investigate the effect of interfering with the conditions that prevail in the smoker’s environment. The researcher makes an assumption that the number of cigarettes smoked could be influenced by either threatening the smokers through intervention or encouraging them by issuing a brochure that guides them on how to smoke which might also include the advantages accruing from smoking. Two schools are randomly selected and data is collected on either the reduction or increase of smoking rate from these two changes in conditions. The first step in this study would be to collect data and from the collected sample and this won’t cause a problem since strategies have been set.
Data collection results to its analysis, after which individual’s interpret to come up with the end results of the study. The process of analyzing data involves hypothesis testing and the conclusion would be either rejecting or accepting it. Hypothesis testing involves several steps as outlined below.
The first step in hypothesis testing is stating the null and alternative hypothesis. The null hypothesis involves converting problem statement into to a mathematical issue. In our case since we expect invention will reduce the average smoking rate by five. Our null hypothesis would thus be stated as the H0 = µ ≤ 25; µ refers to the average smokers in the whole population. The alternative statement refers to the difference in the stated problem and thus in our case it is the mean of the smokers would reduce by anything less than five. H1= µ >25. The next step in hypothesis testing is putting the data to a test static. Either the Z or the F statistic test could be used and the conclusions are made from it.
References
Wilcox, R. R. (2005). Introduction to robust estimation and hypothesis testing. Amsterdam: Elsevier/Academic Press
Sng, H. Y. (2010). Economic growth and transition: Econometric analysis of Lim's S-curve hypothesis. Singapore: World Scientific Pub.
Lemey, P., Salemi, M., & Vandamme, A.-M. (2009). The phylogenetic handbook: A practical approach to phylogenetic analysis and hypothesis testing. Cambridge: Cambridge University Press
