Question

assume that 30% of city employees in city a ride the bus to work. consider the following two statements: the percentage of city employees who ride the bus to work is 10% higher in city b than in city a. the percentage of city employees who ride the bus to work is 10 percentage points higher in city b than in city a. for each case, state the percentage of city employees in city b who ride the bus to work. briefly explain why the two statements have different meanings. when the percentage of city employees who ride the bus to work is 10% higher in city b than in city a, what percentage of city employees in city b ride the bus to work? 33% (type an integer or a decimal.) when the percentage of city employees who ride the bus to work is 10 percentage points higher in city b than in city a, what percentage of city employees in city b ride the bus to work? 40% (type an integer or a decimal.) percentage points describe change or difference, and percent (or %) describes change or difference.

Explanation:

Step1: Calculate percentage for 10% higher

We find 10% of 30% first. 10% of 30% is $0.1\times0.3 = 0.03$. Then we add it to 30% (0.3). So, $0.3+0.03=0.33$ or 33%.

Step2: Calculate percentage for 10 percentage - points higher

We simply add 10 percentage - points to 30%. Since 30% + 10 percentage - points = 40%.

Step3: Explain the difference

Percentage points describe an absolute change or difference. For example, going from 30% to 40% is a 10 - percentage - point increase. Percent (or %) describes a relative change or difference. When we say 10% higher than 30%, we are taking 10% of 30% and adding it to 30%.

Answer:

Percentage points describe an absolute change or difference, and percent (or %) describes a relative change or difference.