Question

A $96\%$ confidence interval for the proportion of the labor force that is unemployed in a certain city is $(0.07,0.10)$. Which of the following statements about this interval is true?

(a) The probability is$0.96$that between $7\%$ and $10\%$of the labor force is unemployed.

(b) About$96\%$ of the intervals constructed by this method will contain the true proportion of unemployed in the city.

(c) The probability is $0.04$that less than $7\%$or more than $10\%$ of the labor force is unemployed.

(d) The true rate of unemployment lies within this interval$96\%$ of the time.

(e) Between $7\%$ and $10\%$of the labor force is unemployed $96\%$ of the time.

Short answer

(b) About $96\%$of the intervals constructed by this method will contain the true proportion of unemployed in the city.

Step-by-step solution

Given Information

Need to find which of the following is true.

Explanation

The upper and lower limit of the confidence intervals are composed of random variables and are subject to uncertainty. Once a sample is collected, we fix the values and calculate the upper and lower bound of the confidence interval. Since they already give you an interval, it's either yes or no whether or not that true population proportion is inside the interval. However, if we were to repeat this method numerous times, about $96\%$ of the intervals will contain the true proportion of unemployed in the city.