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Some assumptions that must be made in order to use a sample to describe a population is to ensure that an accurate sample of the population has been taken. Some factors that must be taken in to account include: gender, race, ethnicity, age, and any other factors that may affect the outcome of the total population. Also the number of sample in relation to the population is also a big factor. Usually, census services use population ratios of per 1000 people.
Stratified sampling is used where the population to be sampled can be divided into subsets, called strata, according to some criterion. Each of these strata are then treated as population and random samples representing the same sampling proportion are taken from each stratum. This ensures that in the overall sample, the number from each stratum is proportional to the size of the stratum in the population. So, for example, if the population consists of 100 boys and 150 girls and you want a sample of 25. The overall sampling proportion is 25/(100+150) = 25/250 = 1/10. So the sampling procedure is to take a simple random sample of 10 boys out of 100 and a simple random sample of 15 girls out of 150. If the whole sample were selected randomly, there is only a 17% probability that it would have been 10 boys and 15 girls. Stratification ensures both genders are represented proportionally in the sample.
Population and SamplePopulation is the area in which you are trying to get information from. Sample is a section of your population that you are actually going to survey. It is important to have a sample that will represent your entire population in order to minimize biases. For example: You want in know how American citizens feel about the war in Iraq. Your population: The United States Your sample: 500 citizens selected randomly from each state.Since the answers all over the US would greatly vary, it is important to have everyone in the population represented in your sample. This is usually done through random sampling, which assumes no biases seeing as the subjects were selected at random.
Sampling can be more accurate than a census as there is greater control of interviewers and less chances of mistakes being made as the data is collated
1. In a random sample of 200 persons of a town, 120 are found to be tea drinkers. In a random sample of 500 persons of another town, 240 are found to be tea drinkers. Is the proportion of tea drinkers in the two towns equal? Use 0.01 level of significance.