Question 43·Easy·Inference from Sample Statistics and Margin of Error
A company has 80 employees. A simple random sample of 25 employees was selected, and 8 of those surveyed said they usually ride a bicycle to work.
Based on this sample, what is the best estimate of the total number of employees at the company who usually ride a bicycle to work?
For questions that ask you to estimate a total from a sample, first compute the sample proportion (e.g., number with a trait ÷ sample size), then multiply that proportion by the total population size to get an estimate. Do the arithmetic carefully, and if the result is not a whole number but represents a count of people, round to the nearest whole number before matching to the answer choices.
Hints
Start with the sample
In the sample of employees, how many ride a bicycle to work? What fraction of the sample is that?
Use a proportion
Assume that the same fraction of all employees rides a bicycle to work. How can you use the fraction from the sample to estimate a number out of ?
Do the multiplication carefully
Write an expression that is "(fraction who bike) × 80" and evaluate it. Then think about how to handle a non-integer result when you are counting people.
Desmos Guide
Compute the estimate directly
In Desmos, type the expression (8/25)*80 into a new line. Look at the numerical output; that value is the estimated number of employees who usually ride a bicycle to work, which you then round to the nearest whole number.
Step-by-step Explanation
Find the sample proportion
From the sample, out of employees usually ride a bicycle to work. This means the sample proportion of bike riders is
This fraction represents the estimated fraction of all employees who bike to work, assuming the sample is representative.
Apply the proportion to the whole company
Use this sample proportion to estimate the number of bike riders among all employees. Multiply the total number of employees by the proportion:
Compute step by step:
Compute and choose the closest whole number
Now divide by :
We cannot have of a person, so we round to the nearest whole number. rounds to , so the best estimate of the total number of employees who usually ride a bicycle to work is 26.