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Why are random samples more representative of the population than other kinds of samples?
A 'random' sample - covers all age groups, genders, and other criteria. A 'targeted' sample might only cover a small part of the population.
Difference between sample regression and population regression line?
AnswerA sample is a subset of a population. Usually it is impossible to test an entire population so tests are done on a sample of that population. These samples can be selected so that they are representative of the population in which cases the sample will have weights, strata, and clusters. But usually people use random samples. So it's not that the line is different, it's that the line comes from different data. In stats we have formulas that allow a sample to represent a population, if you have the entire population (again unlikely), you wouldn't need to use this sample formulas, only the population formulas.
Do small samples and large population variances usually underestimate or be close to population mean?
Small samples and large population variances imply that the estimate for the mean will be relatively poor. Whether or not it will result in an underestimate or overestimate depends on the distribution: with a symmetric distribution the two outcomes are equally likely.
How to reduce sampling error?
The only way to get rid of sampling error is to use the entire population under study. This is usually impossible, so the next best thing is to use large samples and good sampling methods.
Is it true or false that a convenience sample usually consist of respondents with strong opinions?
Yes
