Question

In a recent poll, randomly selected New York State residents at various fast-food restaurants were asked if they supported or opposed a "fat tax" on sugared soda. Thirtyone percent said that they were in favor of such a tax and 66% were opposed. But when asked if they would support such a tax if the money raised were used to fund health care given the high incidence of obesity in the United States, $48\%$ said that they were in favor and $49\%$ were opposed.
(a) In this situation, explain how bias may have been introduced based on the way the questions were worded and suggest a way that the questions could have been worded differently in order to avoid this bias.
(b) In this situation, explain how bias may have been introduced based on the way the sample was taken and suggest a way that the sample could have been obtained in order to avoid this bias.
(c) This poll was conducted only in New York State. Suppose the pollsters wanted to ensure that estimates for the proportion of people who would support a tax on sugared soda were available for each state as well as an overall estimate for the nation as a whole. Identify a sampling method that would achieve this goal and briefly describe how the sample would be taken.

Short answer

(a) The question is, would you approve or oppose a tax on sugared soda that isn't on the diet?

(b) Take a representative sample of all New Yorkers.

(c) A form of sampling known as stratified random sampling includes dividing a population into smaller sub-groups known as strata.

Step-by-step solution

Part (a) Step 1: Given information

To explain how bias may have been created due to the wording of the questions and suggest how the questions could have been worded differently to eliminate this bias.

Part (a) Step 2: Explanation

A random sample of New York state residents was asked whether they supported or opposed a fat tax on sugared drinks at various fast food restaurants. Because the first question was titled "fat tax," some participants may have responded negatively because they mistook it for a tax on people who are overweight. The follow up question gives more details that encourage people to consider the obesity growing epidemic and the enhanced medical services that could be supplied as a tax credit. Instead, it should be "Might you approve or disapprove a tax on non-diet sugary drinks soda?"

Part (b) Step 1: Given information

To describe how bias may have been introduced into the sample as a result of the manner it was taken, and to suggest a strategy to collect the sample in order to eliminate this bias.

Part (b) Step 2: Explanation

A random sample of New York state residents was asked whether they supported or opposed a fat tax on sugared drinks at various fast food restaurants. Because this method only samples people at fast-food restaurants, the bias may have been introduced by the sampling method. To eliminate this bias, we propose a method for obtaining the sample. They may frequent these establishments because they enjoy the drinks and would rather not pay a tax on their preferred beverages. It's feasible that the number of individuals who oppose a tax will be understated. Instead, we should select a representative sample of all New Yorkers.

Part (c) Step 1: Given information

Determine a sampling strategy that will accomplish this goal and briefly describe how the sample will be collected.

Part (c) Step 2: Explanation

A random sample of New York state residents was asked whether they supported or opposed a fat tax on sugared drinks at various fast food restaurants. This goal could be met with a stratified random sampling strategy, in which each state is its own stratum, and a brief description of how the sample would be taken. Random sampling, as the title suggests, is a sampling technique that splits a population into different sub known as strata. In stratified random sampling, as well as stratification, strata are formed based on shared features or characteristics between many individuals, such as income or educational achievement.