## Related questions with answers

Each sampling method suffers from a form of bias. Identify the bias, tell how the sample statistic might deffer significantly from the population parameter, and suggest how the problem might be corrected. To assess consumer response to its new cereal flavor, a cereal company passes out free samples at a local mall and offers shoppers a $5.00 gift certificate if they will fill out a brief form evaluating the new product. They find that 94% of the respondents like the new flavor.

Solution

VerifiedThere are three types of bias:

$\textbf{Selection or undercoverage bias}$ will exclude part of the population.

$\textbf{Measurement or response bias}$ will use a method that gives different values from the true value.

$\textbf{Nonresponse bias}$ is the result of not having data for everybody in the sample.

We note that the shoppers were given a $\$5.00$ gift certificate if they filled out the form. However, this will influence the shoppers to respond in the favor of their product and thus this method will give values that are different from the true value (that is, the shoppers true opinion is different from their opinion on the form, even if the shoppers don't realize it). This then implies that the sample suffers from $\textbf{measurement or response bias}$.

Note that the sample also suffers from $\textbf{selection or undercoverage bias}$, because people who do not go to the local mall have no chance of being in the sample.

Since people tend to respond more in favor of the product due to the $\$5.00$ gift, we would thus expect that the actual percentage that like the new flavor to be lower than 94%.

The problem could be correctly by randomly selecting people and requesting them to fill out the brief form (without giving a $\$5.00$ gift card and requiring each person to actually fill out the form).

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