A large home improvement store is considering expanding its selection of moving products, such as cardboard boxes and packing tape. The store constructs a 90% confidence interval to estimate the proportion of all customers who have moved houses at least once in the last five years. In the random sample of 620 customers, 201 (32.4%) replied that they had moved at least once in the last five years. The sample yielded the 90% confidence interval (0.293, 0.355) for the proportion of all customers who have moved in the past five years. What is the correct interpretation of this confidence interval?
Answer
A
The store can be 90% confident that a proportion of 0.324 of all customers of this store have moved in the past five years.
B
There is a 90% probability that between 29.3% and 35.5% of all customers of this store have moved in the past five years.
C
There is a 10% chance that less than 29.3% or more than 35.5% of all customers of this store have moved in the past five years.
D
The store can be 90% confident that the interval from 0.293 to 0.355 captures the proportion of all customers of this store who have moved in the past five years.
Explanation
A confidence interval estimates the unknown population proportion, not the sample proportion of 0.324. The correct interpretation is that the store can be 90% confident that the interval from 0.293 to 0.355 contains the proportion of all its customers who moved in the past five years. Choice B is tempting, but after the interval is calculated, the population proportion is fixed; the 90% describes the confidence procedure, not a probability that this particular interval contains it.
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