A sample mean with a margin of error gives a plausible range for the mean of a whole population. A simple random sample lets you use the sample mean to estimate that larger group. Subtract the margin for the low end and add it for the high end. The trap is treating a range for an average as a range for individual households.
Hints
- Hint 1
The sample mean is the average for the households measured. The population mean is the average for all households in the city. Which of those two averages is the planner trying to estimate?
- Hint 2
A margin of error puts the plausible population average the same distance below and above the sample average. What do you get when you subtract the margin once and add it once?
- Hint 3
An interval for a mean describes one average, even though it comes from many households. Does a statement about every household, or about a percentage of households, describe that average?
Step-by-step
Find and interpret the margin-of-error interval
Step 1Identify the average being estimated
No Desmos needed. Each endpoint takes one addition or subtraction. The sample mean is the average for the selected households. Because they were chosen in a simple random sample, their mean can estimate the population mean, the average for all households in the city.
- Step 2
Find the low end
The margin of error says the citywide mean could plausibly be gallons below or above the sample mean. Subtract to find the lower endpoint:
- Step 3
Find the high end
Add the same margin to find the upper endpoint:
- Step 4
Match the interval to what it measures
The interval is about the city's average, not each household's usage. So plausible values for the average daily household water usage across all city households are between and gallons. Choice D.