Question

In 2005, 20.9% of adult Americans smoked cigarettes. By 2010, 19.3% of adult Americans smoked cigarettes. Using these numbers, one news report stated that cigarette smoking had decreased in the United States by 1.6%. Another news report stated that cigarette smoking had decreased in the United States by 7.7%. Which statement below is correct?

a) Cigarette smoking decreased by 1.6%
b) Cigarette smoking decreased by 7.7%
c) Cigarette smoking increased by 1.6%
d) Cigarette smoking increased by 7.7%

Answer 1

The correct statement about the change in cigarette smoking among adult Americans is that smoking decreased by about 7.7% from 2005 to 2010, not just 1.6%. The percentage represents a relative decrease from the original figure. Option b.

Step-by-step explanation:

To ascertain the correct statement about the change in cigarette smoking among adult Americans from 2005 to 2010, we must calculate the percentage decrease of smokers in that period. The initial percentage of smokers in 2005 was 20.9%, and it decreased to 19.3% by 2010.

Hence, the absolute decrease in the percentage of smokers is 20.9% - 19.3%, which equals 1.6%. However, to find the relative decrease as a percentage of the original number, we use the formula for percentage change: (New Value - Original Value) / Original Value × 100%.

The calculation would be: ((19.3 - 20.9) / 20.9) × 100% = (-1.6 / 20.9) × 100% ≈ -7.655%. The negative sign indicates a decrease, and we can therefore conclude that there was approximately a 7.7% decrease in the proportion of adult smokers. So, the correct answer is (b) Cigarette smoking decreased by 7.7%.