A large home improvement store is considering expanding its selection of moving products, such as cardboard boxes and packing ta
pe. 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
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 5 years.
Step-by-step explanation:
The confidence interval provides a range of values (lower and upper bound) based on a certain confidence level at which the true proportion or mean value of a given sample mean or proportion exists. In the scenario above, the confidence level is 90% and the confidence interval is 0.293 to 0.355. Hence, we can be 90% confident that the true proportion of all customers of the store who have moved within the last five years exists within this interval.
