An inspector inspects large truckloads of potatoes to determine the proportion with blemishes prior to using the potatoes to make potato chips. She intends to compute a 95% confidence interval for this proportion. To do so, she selects a simple random sample of 90 potatoes, and finds 12 with blemishes. The 95% confidence interval is (0.063, 0.204). What is the correct interpretation for this confidence interval?
Answer
A
The inspector can be 95% confident that the proportion of potatoes with blemishes is 0.133.
B
In 95% of samples taken, between 6.3% and 20.4% of the sampled potatoes would have blemishes.
C
The inspector can be 95% confident that the interval from 0.063 to 0.204 captures the proportion of all potatoes on the truck with blemishes.
D
There is a 5% probability that the proportion of all potatoes that have blemishes is either below 0.063 or above 0.204.
Explanation
A 95% confidence interval estimates the true proportion of blemished potatoes in the truckload. The correct interpretation is that the inspector can be 95% confident that the interval from 0.063 to 0.204 captures that population proportion. The interval does not describe the proportion in 95% of individual samples, and it does not mean there is a 5% probability that the fixed population proportion lies outside this particular interval.
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