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

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Dropping out You have data from interviews with a random sample of students who failed to graduate from a particular college in 7years and also from a random sample of students who entered at the same time and did graduate. You will use these data to compare the percentages of students from rural backgrounds among dropouts and graduates.

A certain candy has different wrappers for various holidays. During Holiday 1the candy wrappers are 30%silver, 30%red, and 40%pink. During Holiday 2the wrappers are 50%silver and 50%blue. Forty pieces of candy are randomly selected from the Holiday 1distribution, and 40 pieces are randomly selected from the Holiday 2 distribution. What are the expected value and standard deviation of the total number of silver wrappers?

A random sample of 200 New York State voters included 88 Republicans, while a random sample of 300 California voters produced 141 Republicans. Which of the following represents the 95%confidence interval that should be used to estimate the true difference in the proportions of Republicans in New York State and California?

(a) (0.44-0.47)±1.96(0.44)(0.56)+(0.47)(0.53)200+300

(b) (0.44-0.47)±1.96(0.44)(0.56)200+(0.47)(0.53)300

(c) (0.44-0.47)±1.96(0.44)(0.56)200+(0.47)(0.53)300

(d)(0.44-0.47)±1.96(0.44)(0.56)+(0.47)(0.53)200+300

(e) (0.44-0.47)±1.96(045)(0.55)1200+1300

The two-sample t statistic for the road rage study (male mean minus female mean) is t=3.18. The P-value for testing the hypotheses from the previous exercise satisfies

(a) 0.001<P<0.005.

(b) 0.0005<P<0.001.

(c) 0.001<P<0.002.

(d) 0.002<P<0.01.

(e) P>0.01.

45. Paying for college College financial aid offices expect students to use summer earnings to help pay for college. But how large are these earnings? One large university studied this question by asking a random sample of 1296students who had summer jobs how much they earned. The financial aid office separated the responses into two groups based on gender. Here are the data in summary form:

(a) How can you tell from the summary statistics that the distribution of earnings in each group is strongly skewed to the right? A graph of the data reveals no outliers. The use of two-sample t procedures is still justified. why?
(b) Construct and interpret a 90%confidence interval for the difference between the mean summer earnings of male and female students at this university.
(c) Interpret the 90%confidence level in the context of this study.

See all solutions

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free