The maker of a cell phone screen protector would like to estimate the proportion of customers who file a warranty claim. To do so, they select a random sample of 200 customers and determine that the 96% confidence interval for the true proportion of customers who file a warranty claim to be 0.15 to 0.28. Which of these statements is a correct interpretation of the confidence level?
Answer
A
Approximately 96% of customers file a warranty claim.
B
The cell phone screen protector maker can be 96% confident that the interval from 0.15 to 0.28 captures true proportion of customers who file a warranty claim.
C
If many random samples of size 200 are selected from the population of all customers, approximately 96% of the sample proportions of customers who file a warranty claim will be between 0.15 and 0.28.
D
If many random samples of size 200 are selected from the population of all customers, about 96% of the intervals constructed from the samples would capture the true proportion of customers who file a warranty claim.
Explanation
A 96% confidence level describes how often the interval-building method succeeds over many repeated random samples. If the maker repeatedly took samples of 200 customers and constructed an interval each time, about 96% of those intervals would contain the true proportion of customers who file a warranty claim. It does not mean that 96% of customers file claims, or that 96% of sample proportions fall in this particular interval.
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