The chamber of commerce for a beach town asked a random sample of city-dwellers, "Would you like to live at the beach?” Based on this survey, the 95% confidence interval for the population proportion of city-dwellers who would like to live at the beach is (0.56, 0.62).Interpret the confidence interval.
Answer
A
95% of city-dwellers would like to live at the beach approximately half of the time.
B
We are 95% confident that approximately half of all city-dwellers would like to live at the beach.
C
95% of the time between 56% and 62% of city-dwellers would like to live at the beach.
D
We are 95% confident that the interval from 0.56 to 0.62 captures the true proportion of city-dwellers who would like to live at the beach.
Explanation
A 95% confidence interval estimates the population proportion, not the percentage of people or surveys that fall within a range. Here, the interval from 0.56 to 0.62 means we are 95% confident that it contains the true proportion of all city-dwellers who would like to live at the beach. This is choice D.
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