1. When someone says they are going to us a sample to draw an inference about a population, it means that rather than survey the entire population, they'll survey a smaller group and apply the results to a larger group. For example, if you take a neighborhood in a town with 100 homes and survey approximately 80% of the households and 76% of those families own multiple televisions you may infer that the majority of the 100 home neighborhood also own multiple televisions. A simple random sample is important for this overall process because the neighborhood above, is a subset of the overall neighborhood (100 houses) and the 80% of the households interviewed regarding the number of televisions in their home had an equal chance of being selected for the analysis.
If you wanted to do a random sample of the students in the cafeteria, you need to look at the students in aggregate in the cafeteria, and not apply a stratified initial pass/approach (those who order Diet Pepsi with their lunch. Looking at the students in the cafeteria, and then applying a distinct subgroup for “Diet Pepsi drinkers” share the same characteristic and have been “stratified.
For this reason, stratifiying the Diet Pepsi drinkers from the cafeteria population you are eliminating the randomness of the population.
Regarding the statement “ A random sample is like a mini population whereas samples that are not random are likely to be biased” - using data from only part of the population of interest, is a sample of the population. There is no applied bias, because this is a random group of the population. If samples are not random, there could be a bias on their participation in the survey or census, for example.
(a) Simple Random Sample - this could be used for a neighborhood census, or anytime of census, where there could be a random sampling of the grouped population. (b) Stratified Sample - a group within a stated population as above - the students in the cafeteria who drink...
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