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Fifty percent of a sample of 500 customers rate the customer service in your store as 'very good'. You calculate a 95% confidence interval with a margin of error $\pm$3%.
Which of the following statements offers the best interpretation?
The 3% margin of error is a standard error for all sample sizes. We are 95% sure the percentage of customers who rate the store service as 'very good' is between 47-53%.
We are 95% sure this sample size represents the entire population.
We are 92-98% confident that 50% of our customers rate our service as 'very good'.
If a survey of 500 customers were conducted 100 times, the percentage who say service is 'very good' will range between 47 and 53 percent 95% of the time.