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Chapter 10: Q. 18 (page 669)

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 0.96that 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 0.04that 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 unemployed96% of the time.

Short Answer

Expert verified

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

01

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.

02

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

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