To find out what proportion of Americans support proposed Medicare legislation to help pay medical costs, the AARP conducted a survey of their members (people over age $50$who pay membership dues). One of the questions was: “Even if this plan won’t affect you personally either way, do you think it should be passed so that people with low incomes or people with high drug costs can be helped?” Of the respondents, $75\%$answered “Yes.”

a. Describe how undercoverage might lead to bias in this study. Explain the likely direction of the bias.

b. Describe how the wording of the question might lead to bias in this study. Explain the likely direction of the bias.

The under coverage may lead to bias in this study and likely direction of this bias.

Chosen or under coverage bias would exclude part of the population.

The survey is only including the people over the age of $50$whom paying membership dues and therefore the people under the age of $50$are excluded, which is leading to under coverage bias.

People over the age of $50$are the most likely to answer “Yes”, the reason is that they are the most likely to have higher drug costs and therefore they would benefit of the plan. This then implies that the sample with under coverage bias would overestimate the proportion of Americans who would help the plan.

Measurement or response bias would use a method which gives different values from the true value.

The questions causes response bias because of the statement “can be helped” in the question, which would affect the people to say “Yes” as some people would generally want to support other people

This then implies that the sample with response bias would overestimates the proportion of Americans who help the plan.