MAT201: Week 4 Case Study



MAT201: Week 4 Case Study

The sampling used in this study is stratified because students were first divided up by class (strata) i.e. almost 10% of each sample, and then they are selected at random which resulted in 49 sophomore from 496, 34 Junior from 348 and 48 senior students from a total of 481 students. The objective is to achieve stratified sampling with small samples as representative of the distribution as possible. Thus it is possible to reduce the number of simulations for a given accuracy of measurement, or viewed another way to increase the accuracy of the results for a given number of simulations. In the case of a continuous random variable defined in a real interval, for example [1, 348] junior students, this interval breaks down into a number of subintervals disjoint and whose union is the domain of the variable, for example, [0,100], [101, 200], [201, 300] and [301, 348]. Almost 10% sample has been taken from each strata i.e. n1, n2, n3 and n4 respectively. The intervals n1 n2, n3 and n3 should be approximately equal to the product of the variance within these ranges by the probability of each. Stratified sampling is essentially pre-determine how many elements of the sample will be drawn from each stratum. The pre-determination can be made in various ways, the most common being referred to as uniform (where draws an equal number of elements in each layer) and proportional (where the number of elements drawn in each stratum is proportional to the number of elements in stratum). Stratified sampling is recommended even if the strata of the population are at least approximately the same size. Otherwise, it will be preferable because the stratification proportional to provide a more representative sample of the population.

The sampling used in this study is random because random sample is one sample to the formation of which there was a procedure for selecting elements or group of elements in a manner which gives each element of the population probability of inclusion in the sample calculated and nonzero. And in this sampling each contestant has an equally-likely chance of being chosen and each sample of size three have an equally likely chance of being chosen. For e.g. 2,000 people interviewed by telephone on behalf of all Germans over the age of 18, a representative cross-section corresponds to the population. For the selection of ...