Heather runs a successful lawn-mowing business. She would like to estimate the true mean amount of time it takes for her employees to mow a lawn. To do so, she selects a random sample of 30 customers and records the time it takes the employees to mow their lawns. The 90% confidence interval for the true mean time it takes her employees to mow a lawn is 40 to 55 minutes. Which of these statements is a correct interpretation of the confidence level?
Answer
A
Approximately 90% of the customers have lawns that take between 40 and 55 minutes to mow.
B
There is a 90% probability that the true mean time it takes for her employees to mow a lawn is between 40 and 55 minutes.
C
If many random samples of size 30 are selected from the population of all customers, approximately 90% of the sample mean times for her employees to mow the lawns will be between 40 and 55 minutes.
D
If many random samples of size 30 are selected from the population of all customers, approximately 90% of the constructed intervals would capture the true mean time it takes for her employees to mow a lawn.
Explanation
A 90% confidence level describes how often the interval-building method succeeds over many repeated random samples. If Heather repeatedly took samples of 30 customers and built a confidence interval each time, about 90% of those intervals would contain the true mean mowing time. The confidence level does not mean that 90% of individual lawns take 40 to 55 minutes, nor that this particular fixed interval has a 90% probability of containing the mean.
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