A city planner would like to estimate the true mean annual income of all households in the city. She selects a random sample of 50 households and determines that the 99% confidence interval for the true mean annual income of all households in the city to be $42,000–$68,000. Which of these statements is a correct interpretation of the confidence level?
Answer
A
Approximately 99% of all households have incomes between $42,000 and $68,000.
B
The city planner can be 99% confident that the true mean annual income for all households in the city is between $42,000 and $68,000.
C
If many random samples of size 50 are selected from all households in the city, approximately 99% of the intervals would capture the true mean household income.
D
Approximately 99% of the sample means, computed from many random samples of size 50 from all households in the city, will fall between approximately $42,000 and $68.000.
Explanation
A 99% confidence level describes how often the interval-building method succeeds over repeated random samples. If many samples of 50 households were taken and a confidence interval calculated from each one, about 99% of those intervals would contain the true mean income. Choice B is a common informal description for this particular interval, but choice C precisely explains what the confidence level means.
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