/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q.2 Thirty-five people from a random... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Q.2 (page 664)

Thirty-five people from a random sample of 125workers from Company A admitted to using sick leave when they weren鈥檛 really ill. Seventeen employees from a random sample of 68workers from Company B admitted that they had used sick leave when they weren鈥檛 ill. A 95% confidence interval for the difference in the proportions of workers at the two companies who would admit to using sick leave when they weren鈥檛 ill is

(a) 0.03卤(0.28)(0.72)125+(0.25)(0.75)68

(b) localid="1650367573248" 0.03卤1.96(0.28)(0.72)125+(0.25)(0.75)68

(c) 0.03卤1.645(0.28)(0.72)125+(0.25)(0.75)68

(d)

0.03卤1.96(0.269)(0.731)125+(0.269)(0.731)68

(e) 0.03卤1.645(0.269)(0.731)125+(0.269)(0.731)68

Short Answer

Expert verified

The correct answer is (b)0.03卤1.96(0.28)(0.72)125+(0.25)(0.75)68.

Step by step solution

01

Given Information

x1=35

n1=125

x2=17

n2=68

c=95%

02

Explanation

The sample proportion is the number of successes divided by the sample size:

p^1=x1n1

=35125

=0.28

localid="1650367755652" p^2=x2n2

=1768

=0.25

For confidence level 1-伪=0.95, determine z伪/2=z0.025using table II (look up 0.025in the table, the z-score is then the found z-score with opposite sign):

z伪/2=1.96

The endpoints of the confidence interval for p1-p2are then:

localid="1650367861788" p^1-p^2卤z伪/2路p^11-p^1n1+p^21-p^2n2=(0.28-0.25)卤1.960.28(1-0.28)125+0.25(1-0.25)68

=0.03卤1.960.28(0.72)125+0.25(0.75)68

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 91影视!

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

Many new products introduced into the market are targeted toward children. The choice behavior of children with regard to new products is of particular interest to companies that design marketing strategies for these products. As part of one study, randomly selected children in different age groups were compared on their ability to sort new products into the correct product category (milk or juice). Here are some of the data:

Age groupNNumber who sorted correctly4- to 5-year-olds50106- to 7-year-olds5328

Are these two age groups equally skilled at sorting? Use information from the Minitab output below to support your answer.

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.

Mrs. Woods and Mrs. Bryan are avid vegetable gardeners. They use different fertilizers, and each claims that hers is the best fertilizer to use when growing tomatoes. Both agree to do a study using the weight of their tomatoes as the response variable. They had each planted the same varieties of tomatoes on the same day and fertilized the plants on the same schedule throughout the growing season. At harvest time, they each randomly select 15tomatoes from their respective gardens and weigh them. After performing a two-sample t-test on the difference in mean weights of tomatoes, they get t=5.24and P=0.0008. Can the gardener with the larger mean claim that her fertilizer caused her tomatoes to be heavier?

(a) No, because the soil conditions in the two gardens is a potential confounding variable.

(b) No, because there was no replication.

(c) Yes, because a different fertilizer was used on each garden.

(d) Yes, because random samples were taken from each garden.

To study the long-term effects of preschool programs for poor children, researchers designed an experiment. They recruited 123children who had never attended preschool from low-income families in Michigan. Researchers randomly assigned 62of the children to attend preschool (paid for by the study budget) and the other 61to serve as a control group who would not go to preschool. One response variable of interest was the need for social services for adults. In the past 10years, 38children in the preschool group and 49 in the control group have needed social services.4 1. Does this study provide convincing evidence that preschool reduces the later need for social services? Carry out an appropriate test to help answer this question.

How quickly do synthetic fabrics such as polyester decay in landfills? A researcher buried polyester strips in the soil for different lengths of time, then dug up the strips and measured the force required to break them. Breaking strength is easy to measure and is a good indicator of decay. Lower strength means the fabric has decayed. For one part of the study, the researcher buried 10strips of polyester fabric in well-drained soil in the summer. The strips were randomly assigned to two groups: 5of them were buried for 2weeks and the other 5were buried for 16weeks. Here are the breaking strengths in pounds

Do the data give good evidence that polyester decays more in 16weeks than in 2weeks? Carry out an appropriate test to help answer this question .
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation
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.