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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 is0.96that between 7% and 10%of the labor force is unemployed.

(b) About96% 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 interval96% of the time.

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

Short Answer

Expert verified

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

Step by step solution

01

Given Information

Need to find which of the following is true.

02

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.

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Most popular questions from this chapter

Shortly before the2008 presidential election, a survey was taken by the school newspaper at a very large state university. Randomly selected students were asked, “Whom do you plan to vote for in the upcoming presidential election?” Here is a two-way table of the responses by political persuasion for 1850students:

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