Question 4·Easy·Inference from Sample Statistics and Margin of Error
A polling organization randomly selected 40 households from a city that contains 120,000 households in total. Of the households in the sample, 12 reported that they subscribe to at least one video-streaming service. About how many households in the city would be expected to subscribe to a video-streaming service?
For questions about estimating totals from a sample, first compute the sample proportion (for example, successes divided by sample size), and simplify it to a clear decimal or percent. Then multiply this proportion by the total population size given in the problem. Finally, compare your result to the answer choices, being careful not to round the initial fraction incorrectly, since small percentage errors can lead to entirely different answer choices.
Hints
Use the sample to find a proportion
First, write the number of subscribing households in the sample as a fraction of the total sample size. What fraction is 12 out of 40?
Turn the fraction into a useful form
Simplify or convert it to a decimal or percentage so it is easy to apply to the whole population.
Scale the proportion to the whole city
Once you know what fraction (or percent) of the sample subscribes, multiply that fraction by 120,000 to estimate how many of the city’s households subscribe.
Desmos Guide
Use Desmos to compute the estimate
In Desmos, type 12/40 * 120000 (or 0.3 * 120000) and press Enter. Compare the numerical result that Desmos displays with the answer choices and select the matching one.
Step-by-step Explanation
Interpret the sample information
The poll found that 12 out of 40 sampled households subscribe to at least one video-streaming service. This gives you a sample proportion of subscribing households.
Compute the sample proportion
Find the fraction of households in the sample that subscribe:
- The fraction is .
- Simplify: .
So the sample suggests that about of households subscribe.
Set up the estimate for the whole city
Assuming the sample is representative of the whole city, use the same proportion for all 120,000 households.
- You want of 120,000.
- In decimal form, that is .
Now calculate this product to estimate the number of subscribing households in the city.
Calculate and match to the answer choices
Compute the product:
So you would expect about 36,000 households in the city to subscribe to a video-streaming service. This corresponds to choice C) 36,000.