/*! 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 R8.7. Running red lights A random digi... [FREE SOLUTION] | 91影视

91影视

Running red lights A random digit dialing telephone survey of 880 drivers asked, 鈥淩ecalling the last ten traffic lights you drove through, how many of them were red when you entered the intersections?鈥 Of the 880 respondents, 171 admitted that at least one light had been red.

(a) Construct and interpret a 95% confidence interval for the population proportion.

(b) Nonresponse is a practical problem for this survey鈥攐nly 21.6% of calls that reached a live person were completed. Another practical problem is that people may not give truthful answers. What is the likely direction of the bias: do you think more or fewer than 171of the 880 respondents really ran a red light? Why? Are these sources of bias included in the margin of error?

Short Answer

Expert verified

Part (a) We are 95%confident that the true population proportion is between(0.1682,0.2204)

Part (b) The likely direction was more than 171respondents and no, these sources of bias do not include the margin of error.

Step by step solution

01

Part (a) Step 1: Given information

x=171n=880

02

Part (a) Step 2: Concept

Formula used:p=xn

03

Part (a) Step 3: Calculation

It is given in the question that,x=171n=880

And the sample proportion is calculated as: p=xn=171880=0.1943

For the confidence level 1=0.95and find out z/2=z0.025using table II, we get, z/2=1.96

Thus, the confidence interval is as: pz/2p1-pn=0.19431.960.1943(10.1943)880=0.1682p+z/2p1-pn=0.1943+1.960.1943(10.1943)880=0.2204

Thus, we are 95%confident that the true population proportion is between(0.1682,0.2204)

04

Part (b) Step 1: Calculation

It is given in the question that, x=171n=880

And we're 95%sure the genuine population share is somewhere between(0.1682,0.2204) As a result, most people will be reluctant to admit to running a red light, hence the proportion is likely to be greater, implying that more than 171respondents have really done so. These causes of bias are not sampling errors, and as the margin of error only covers sampling errors, they have been excluded from the margin of error.

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

Starting a nightclub A college student organization wants to start a nightclub for students under the age of 21. To assess support for this proposal, they will select an SRS of students and ask each respondent if he or she would patronize this type of establishment. They expect that about 70% of the student body would respond favorably. What sample size is required to obtain a 90% con铿乨ence interval with an approximate margin of error of 0.04? Show your work

2K10 begins In January 2010, a Gallup Poll asked a random sample of adults, "In general, are you satisfied or dissatisfied with the way things are going in the United States at this time?" In all, 256said that they were sitisfied and the remaining 769said they were not. Construct and interpret a90%confidence interval for the proportion of adults who are satisfied with how things are going. Follow the four-step process.

Bone loss by nursing mothers.: Breastfeeding mothers secrete calcium into their milk. Some of the calcium may come from their bones, so mothers may lose bone minerals. Researchers measured the per cent change in bone mineral content (BMC) of the spines of 47randomly selected mothers during three months of breastfeeding. The mean change in BMC was 3.587%and the standard deviation was 2.506%.

(a) Construct and interpret a 99% confidence interval to estimate the mean per cent change in BMC in the population.

(b) Based on your interval from (a), do these data give good evidence that on average nursing mothers lose bone minerals? Explain

Can you taste PTC? PTC is a substance that has a strong bitter taste for some people and is tasteless for others. The ability to taste PTC is inherited. About 75% of Italians can taste PTC, for example. You want to estimate the proportion of Americans who have at least one Italian grandparent and who can taste PTC.

(a) How large a sample must you test to estimate the proportion of PTC tasters within 0.04with 90% con铿乨ence? Answer this question using the 75% estimate as to the guessed value for p.

(b) Answer the question in part (a) again, but this time use the conservative guess p=0.5. By how much do the two sample sizes differ?

Researchers were interested in comparing two methods for estimating tire wear. The first method used the amount of weight lost by a tire. The second method used the amount of wear in the grooves of the tire. A random sample of 16tires was obtained. Both methods were used to estimate the total distance traveled by each tire. The table below provides the two estimates (in thousands of miles) for each tire.

(a) Construct and interpret a 95%confidence interval for the mean difference in the estimates from these two methods in the population of tires.

(b) Does your interval in part (a) give convincing evidence of a difference in the two methods of estimating tire wear? Justify your answer.

role="math" localid="1649913699288" TireWeightGrooveTireWeightGroove145.935.7930.423.1241.939.21027.323.7337.531.11120.420.9433.428.11224.516.1531.024.01320.919.9630.528.71418.915.2730.925.91513.711.5831.923.31611.411.2

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.