A sample proportion is the share of surveyed people with a particular trait. For a random sample, use that share to estimate the share in the whole population. Divide by the sample size, then multiply by the population size. Desmos can handle the arithmetic. The tempting slip is to report the sample percentage as a count of people.
Hints
- Hint 1
A sample proportion compares the people with the trait to everyone surveyed. Divide the bicycle riders by the surveyed employees, not by all employees.
- Hint 2
Because the sample was chosen at random, its share is a reasonable estimate for the company’s share. What happens when you multiply that share by the company’s employees?
- Hint 3
An employee count must be a whole number. If your calculation falls between two integers, round to the nearest one.
Step-by-step
Scale the sample share
Step 1Find the share in the sample
The sample proportion is the number who ride a bicycle divided by the number surveyed. Type in Desmos; it shows , or . The denominator is because the riders came from those surveyed employees.
- Step 2
Estimate the company-wide count
The sample was selected at random from the company, so use its share to estimate the share of all employees. Type on the next Desmos line. It shows , the estimated number of employees who ride a bicycle.
- Step 3
Give a whole-person estimate
You can't count a fraction of an employee, so round to the nearest whole number. The best estimate is employees who usually ride a bicycle to work. Choice C.