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

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

Step-by-step solution

Given Information

We are given that 96% confidence interval for the proportion of the labor force that is unemployed is .

We have to find out the statement which is true about the interval.

Explanation

As we know that the upper limit and lower limit are composed of random variables and are subjected to uncertainty and when we collect the sample the values are fixed and then we calculate the limit bound of the confidence interval and if we will use this method various times than $96\%$of the intervals will contain the true proportion of unemployed in the city.

Hence, statement (b) is true