An estimated mean from a random sample points to a population mean, the average of the whole group. Subtract and add the given margin of error to find a plausible interval, using Desmos to check the endpoints. Look for a likely claim about the average, not a guarantee about every individual value: uncertainty in an estimate is different from variation among individuals.
Hints
- Hint 1
A sample is a smaller group chosen from a larger group. Random selection helps a sample statistic represent the larger group, though individual apples can differ from their group's average. What statistic did the researcher estimate?
- Hint 2
A margin of error goes below and above the estimate. Use for one endpoint and for the other. Which is the lower endpoint, and which is the upper?
Step-by-step
Build and interpret the mean interval
Step 1Identify what the estimate describes
The randomly chosen apples are a sample, a smaller group from the orchard. Their -kilogram mean (average) estimates the population mean, the average mass across all apples in the orchard.
- Step 2
Put the margin around the estimate
A margin of error gives a plausible distance on either side of an estimate. So put kilogram below and above kilogram:
These bounds are for the orchard's average, not for each apple's mass.
- Step 3
Find the lower endpoint
Type in Desmos. It shows , the lower end of the plausible range for the orchard's average mass.
- Step 4
Find the upper endpoint
Add on the next Desmos line. It shows , the upper end of that range.
- Step 5
Choose the supported conclusion
The average mass of all apples in the orchard is likely between and kilogram. “Likely” fits an estimate; the data don't guarantee a mass for any individual apple. Choice C.