Problem-Solving and Data AnalysisVery hardInterpreting a confidence interval
Problem-Solving and Data Analysis practice question
From a random sample, researchers estimate that the mean height of adult men in a city is 176 centimetres, with a 95% confidence interval from 174 to 178 centimetres. Which statement is the best interpretation of this interval?
- A. It is plausible that the mean height of all adult men in the city lies between 174 and 178 centimetres.Correct
- B. 95 percent of adult men in the city are between 174 and 178 centimetres tall.
- C. Every adult man in the sample is between 174 and 178 centimetres tall.
- D. The mean height of adult men in the city is exactly 176 centimetres.
Answer: A. It is plausible that the mean height of all adult men in the city lies between 174 and 178 centimetres.
The interval is about the population mean, not about individuals.
Why the other answers are wrong
- B. 95 percent of adult men in the city are between 174 and 178 centimetres tall.
- Individual heights spread far wider than the interval for the mean.
- C. Every adult man in the sample is between 174 and 178 centimetres tall.
- The interval does not bound individual heights.
- D. The mean height of adult men in the city is exactly 176 centimetres.
- 176 is an estimate, not a certainty.
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