Question

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?the inspector can be 95% confident that the proportion of potatoes with blemishes is 0.133.in 95% of samples taken, between 6.3% and 20.4% of the sampled potatoes would have blemishes.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.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 for a population proportion means we are 95% confident that the interval contains the true population proportion. The sample proportion here is $\frac{12}{90} \approx 0.133$, but this is the point estimate, not what the interval interprets. The interval (0.063, 0.204) refers to the range we believe contains the true proportion of all potatoes on the truck with blemishes, not just sampled ones. The 95% confidence level does not refer to the probability the true proportion is outside the interval, nor does it describe sample proportions in repeated sampling in the way the incorrect options state.

Answer:

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.