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 non-diet sugared soda. Thirty-one 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 they 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 non-diet 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 first question was called a "fat tax" then people may have reached negatively therefore they may have thought that this is a tax for overweight individuals.

The second question provides extra information that gets people thinking about the obesity epidemic in the US and the increased health care that could be provided as a benefit with the tax money instead try "would you support or oppose a tax on non-diet sugared soda.

(b) The given statement is proved below.

(c) Use a stratified random sapling technique where each state is its own stratum.

Step-by-step solution

Part (a) step 1: Given information

We need to find bias may have been introduced based on the way the questions were worded and suggest a way that they could have been worded differently in order to avoid this bias.

Part (a) step 2: Explanation

The first question was called a "fat tax" then people may have reacted negatively so they may have thought that is a tax for overweight individuals.

The second question provides extra information that gets people thinking about the obesity epidemic in the US and the increased health care that could be provided as a benefit with the tax money instead try "would you support or oppose a tax on non-diet sugared soda?

Part (b) step 1: Given information

We need to find 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.

Part (b) step 2: Explanation

This method samples only people at fast-food restaurants. They may go to these restaurants because they like the drinks and wouldn't want to pay a tax on their favorite beverages. It is the proportion of those who would oppose a tax that will be overestimated.

Instead, take a random sample of all New York residents.

Part (c) step 1: Given information

We need to find the pollsters wanted to ensure that estimates for the proportion of people who would support a tax on non-diet sugared soda were available for each state as well as an overall estimate for the nation as a whole.

Part (c) step 2: Explanation

Use stratified random sampling technique there each state is its own stratum.