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Sampling bias occurs when certain members of a population are more likely to be included in a sample than others. This leads to a sample that does not accurately represent the population. In the context of surveys and polls, sampling bias can arise if the selection process favors certain outcomes or classes within the population.

For instance, if a poll is conducted only over the phone during working hours, it may not adequately represent individuals who are not at home during that time, such as working professionals. This results in a sampling bias because the sample does not accurately reflect the diversity of the intended population.

• Selection Bias: Occurs when the method used to select participants leads to a non-representative sample.
• Nonresponse Bias: When certain individuals do not respond to the survey, possibly leading to a skewed result.
• Voluntary Response Bias: When individuals self-select into the sample, often leading to opinions that are not representative of the general population.

In the exercise, however, the random selection method used minimizes the risk of such biases.

Chance plays a significant role in sampling, especially when selecting a random sample. It refers to the possibility that the chosen sample results might differ from the true values of the entire population due to random variation. The concept of chance acknowledges that even a perfectly randomized sample can yield results that differ slightly from the actual population parameters.

In statistics, this randomness is normal and expected, and any observed deviation is often referred to as 'sampling error.' A small sample size or a high level of variability within the population can make such sampling errors more apparent.

• Random Variation: Differences in the sample that occur by chance rather than by deliberate bias.
• Sampling Error: The error caused by observing a sample instead of the whole population.

In the Cleansburg example, differences between the poll results and election outcomes could be due to chance rather than any flawed sample selection process.

Random sampling is a technique used to ensure that every individual in a population has an equal chance of being selected for the sample. This method helps mitigate the effects of sampling bias, providing a fair representation of the population.

Random sampling involves various techniques:

• Simple Random Sampling: Every member of the population has an equal probability of being selected. It’s like drawing names out of a hat.
• Systematic Sampling: Selecting every nth member from a list of the population, after a random starting point.
• Stratified Sampling: Dividing the population into subgroups and then randomly sampling from these groups to ensure representation from each subgroup.

The key advantage of random sampling is its ability to produce samples that are likely to be representative of the population, which reduces the likelihood of sampling bias and increases the reliability of the survey results.