Q. AP3.18 A 96% confidence interval for th... [FREE SOLUTION]

91影视

The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 837 pages

ISBN: 9781319113339

Chapter 10: Q. AP3.18 (page 703)

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 is true?
a. The probability is 0.96 that between $7 % a n d 10 %$ of the labor force is unemployed.
b. About $96 %$ of the intervals constructed by this method will contain the true proportion of the labor force that is unemployed in the city.
c. In repeated samples of the same size, there is a $96 %$ chance that the sample proportion will fall between $0.07 a n d 0.10 .$
d. The true rate of unemployment in the labor force lies within this interval 96% of the time.
e. Between $7 % a n d 10 %$ of the labor force is unemployed 96% of the time.

Short Answer

Expert verified

The correct statement is:

b. About $96 %$ of the intervals constructed by this method will contain the true proportion of the labor force that is unemployed in the city.

Step by step solution

Step 1: Given information

We have to tell interval for the proportion of the labor force that is unemployed in a certain city.

Explanation

The confidence intervals' upper and lower limits are made up of random variables and are therefore unpredictable. We fix the values and calculate the upper and lower bounds of the confidence interval once a sample has been gathered. Because they've already given you an interval, the answer is either yes or no as to whether the genuine population proportion falls within it. However, if we apply this procedure several times, we would find that approximately 96 percent of the intervals reflect the genuine proportion of unemployment in the city.