Chapter 10, Problem AP3.18CPT

To determine

The true statement is to be chose which shows that $96\%$ of intervals will contain the true proportion of the unemployed in the city:

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

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

(c) In repeated samples of the same size, there is a $96\%$ chance that the sample proportion will fall between $0.07$ and $0.10$ .

(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.

Answer to Problem AP3.18CPT

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

Explanation of Solution

The upper and lower limit of the confidence intervals are composed of random variables and are subject to uncertainty.

Once a sample is collected, fix the values and calculate the higher and lesser 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, to repeat this method numerous times, about $96\%$ of the intervals will contain the true proportion of unemployed in the city.

Conclusion:

Hence, true statement is shown by option (b).