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Suppose that a 95% confidence interval for the proportion of teen drivers who were involved in a car accident is found to be (0.1425, 0.2875).
-Consider the following statement: "If the sampling procedure were repeated many times, this would result in many different 95% confidence intervals. We would expect that 95% of the time, the true value of the population proportion would fall between 0.1425 and 0.2875." Does this statement correctly interpret the meaning of the 95% confidence level?

Question

Use the following information for questions:
 Suppose that a 95% confidence interval for the proportion of teen drivers who were involved in a car accident is found to be (0.1425, 0.2875).
-Consider the following statement: "If the sampling procedure were repeated many times, this would result in many different 95% confidence intervals. We would expect that 95% of the time, the true value of the population proportion would fall between 0.1425 and 0.2875." Does this statement correctly interpret the meaning of the 95% confidence level?

Quizplus · Accepted Answer

The statement incorrectly interprets the meaning of the 95% confidence level. The correct interpretation is that if we were to take many samples and construct a 95% confidence interval from each, 95% of those intervals would contain the true population proportion. The interval (0.1425, 0.2875) is just one of these possible intervals, and the true proportion is either within this specific interval or not; the percentage does not apply to the interval itself but to the process over many samples.

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