Chapter 12, Problem 43PT4

(a)

To determine

To 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.

Explanation of Solution

It is given that 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 tax and sixty-six percent were opposed. But when asked if they would support such tax if the money raised were used to fund health care given the high incidence of obesity in United States, forty-eight percent said they were in favor and forty-nine percent were opposed. Thus, we can say that the first question was called a "fat tax" so people may have reacted negatively since they may have thought that this is a tax for overweight individuals. And 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. So, instead they should have asked "Would you support or oppose a tax on non-diet sugared soda?" in order to avoid biasness.

(b)

To determine

To explain how bias may have been introduced based on the way sample was taken and suggest a way that the sample could have been obtained in order to avoid this bias.

Explanation of Solution

It is given that 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 tax and sixty-six percent were opposed. But when asked if they would support such tax if the money raised were used to fund health care given the high incidence of obesity in United States, forty-eight percent said they were in favor and forty-nine percent were opposed. Thus, bias may have been introduced based on the way sample was taken because this method samples only people at fast-food restaurants. They may go to these restaurants because they like the drinks and would not any to pay a tax on their favorite beverages. It is likely that the proportion of those who would oppose a tax will be overestimated. Thus, instead they should have taken a random sample of all New York residents so that the sample could have been obtained in order to avoid this bias.

(c)

To determine

To identify a sampling method that would achieve this goal and briefly describe how the sample would be taken.

Answer to Problem 43PT4

We should use stratified sampling method.

Explanation of Solution

It is given that 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 tax and sixty-six percent were opposed. But when asked if they would support such tax if the money raised were used to fund health care given the high incidence of obesity in United States, forty-eight percent said they were in favor and forty-nine percent were opposed. Thus, to achieve this goal the sampling method we should use is stratified sampling method because in this the total population is divided into smaller groups or strata to complete the sampling process so in this case, each state is its own stratum.